Exhibit 10.35

CONSENT AND FIRST AMENDMENT TO CREDIT AGREEMENT

This CONSENT AND FIRST AMENDMENT TO CREDIT AGREEMENT (this “Amendment”) is dated as of March 21, 2012 and is entered into by and among Chuy’s Opco, Inc., a Delaware corporation (“Borrower”), the Persons designated on the signature pages hereto as Guarantors (“Guarantors”), the Lenders party hereto, and GCI Capital Markets LLC, a Delaware limited liability company, as administrative agent for all Lenders (“Administrative Agent”).

W I T N E S S E T H:

WHEREAS, Borrower, Guarantors, Administrative Agent and Lenders are parties to that certain Credit Agreement dated as of May 24, 2011 (as amended, supplemented or otherwise modified from time to time, the “Credit Agreement”; capitalized terms not otherwise defined herein have the definitions provided therefor in the Credit Agreement);

WHEREAS, Borrower has advised Administrative Agent that Borrower desires to make (i) a distribution in an amount not to exceed $23,000,000 (the “Distribution”) to Chuy’s Holdings, Inc., a Delaware corporation (“Holdings”), to allow Holdings to purchase and redeem from various of its shareholders certain Stock of Holdings for an aggregate purchase price of up to $23,000,000 (the “Redemption”) pursuant to terms substantially similar to those set forth in that certain form of Stock Repurchase Agreement, a copy of which is attached hereto as Exhibit A (the “Redemption Agreement”), and (ii) in consideration for the termination of the Management Agreement and all obligations thereunder (other than with respect to Borrower’s obligations pursuant to Sections 3 and 7 and Schedule I thereof), a one-time lump sum payment to Sponsor in an amount not to exceed $2,000,000 (the “Termination Payment”; and collectively with the Distribution and the Redemption, the “Proposed Transactions”) pursuant to the terms of that certain Agreement Relating to Termination of Advisory Agreement dated as of March 21, 2012 between Borrower and Sponsor, a copy of which is attached hereto as Exhibit B (the “Termination Agreement”);

WHEREAS, the Proposed Transactions, without the consent of Administrative Agent and Requisite Lenders, would violate Sections 7.4 and 7.14 of the Credit Agreement;

WHEREAS, in connection with the Proposed Transactions, Borrower has requested that Administrative Agent and Requisite Lenders amend the Credit Agreement to, among other things, provide for an additional draw on the date hereof of $25,000,000 on the Term A Loan such that the outstanding principal amount of Term A Loan is increased on the date hereof from $52,368,750 to $77,368,750; and

WHEREAS, Administrative Agent and the Requisite Lenders have agreed to consent to the Proposed Transactions and to amend the Credit Agreement in certain respects, subject to the terms and conditions contained herein;

NOW THEREFORE, in consideration of the mutual conditions and agreements set forth in the Credit Agreement and this Amendment, and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto hereby agree as follows:

1. Consent. Subject to the satisfaction of the conditions set forth in Section 3 below, and in reliance on the representations and warranties contained in Section 4 below, Administrative Agent and Lenders hereby consent to (a) the Distribution so long as 100% of the proceeds from the Distribution are used by Holdings to finance the Redemption and pay costs and expenses related to the Redemption, (b) the Redemption pursuant to terms substantially similar to those set forth in the Redemption Agreement so long as (i) the Redemption is consummated on or before May 21, 2012, (ii) the Redemption is consummated in accordance with applicable law and with the certificate of incorporation, by-laws and other organizational documents of Holdings and (iii) Sponsor shall receive no more than $9,400,000 in the aggregate from the redemption of Stock held by it pursuant to the Redemption, and (c) the Termination Payment so long as (i) the Management Agreement and all obligations thereunder (other than with respect to Borrower’s obligations pursuant to Sections 3 and 7 and Schedule I thereof) have been, or concurrently with the Termination Payment will be, terminated pursuant to the terms the Termination Agreement and (ii) no Default or Event of Default is in existence at the time of the Termination Payment or would otherwise be caused thereby, in each case without use of or application against any basket or carveout otherwise provided for in the Credit Agreement. Except as expressly set forth in this Amendment, the foregoing consent shall not constitute (i) a modification or alteration of the terms, conditions or covenants of the Credit Agreement or any other Loan Document or (ii) a waiver, release or limitation upon the exercise by Administrative Agent or any Lender of any of its rights, legal or equitable, thereunder.

2. Amendments. Subject to the satisfaction of the conditions set forth in Section 3 below, the Credit Agreement is amended as follows:

(a) Section 2.1(b) of the Credit Agreement is hereby amended and restated in its entirety to read as follows:

(b) Term A Loan.

(i) On the Closing Date, each Term A Loan Lender which then had a Closing Date Term A Loan Commitment made, severally and not jointly, a Closing Date Term A Loan to Borrower in an original principal amount equal to such Term A Loan Lender’s Pro Rata Share of the Closing Date Term A Loan Commitment. Subject to the terms and conditions of this Agreement, on the First Amendment Closing Date, each Term A Loan Lender which has a Second Term A Loan Commitment agrees, severally and not jointly, to make a Second Term A Loan to Borrower in an original principal amount equal to such Term A Loan Lender’s Pro Rata Share of the Second Term A Loan Commitment. Amounts paid or prepaid in respect of the Term A Loan may not be reborrowed.

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(ii) The Term A Loan shall be repaid, beginning on March 31, 2012 and on the last day of each calendar quarter thereafter, in an amount equal to the respective amount set forth opposite the dates indicated below (subject to any prepayments previously made thereof), with the remaining principal amount of the Term A Loan then outstanding due and payable in full on the Term A Loan Maturity Date.

(iii) Notwithstanding the foregoing clause (ii), the entire unpaid balance of the aggregate Term A Loan and all other Term A Loan Obligations shall be due and payable in full on the Term A Loan Maturity Date, if not sooner paid in full in accordance with the terms of the Loan Documents (without limiting Borrower’s obligation to timely make all payments required under the terms of the Loan Documents).

(b) Section 2.4 of the Credit Agreement is hereby amended and restated in its entirety to read as follows:

Section 2.4 Use of Proceeds.

Borrower shall utilize the proceeds of the Loans funded under the Revolving Loan Commitment and the proceeds of the Term A Loan solely for financing the Dividend Recapitalization, funding the Proposed Transactions and the payment of costs and expenses in connection therewith, refinancing certain obligations of Borrower and its Subsidiaries on the Closing Date (as set forth with more specificity on Schedule 2.4), payment of fees, costs and expenses in connection with this Agreement and the Related Transactions and the funding of Borrower’s working capital and for other general corporate purposes (including Capital Expenditures not made in violation of the terms of this Agreement). Schedule 2.4 contains a description

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of Borrower’s sources and uses of funds as of the Closing Date, including Loans and Letter of Credit Obligations to be made or incurred on that date. Borrower shall utilize proceeds of any Delayed Draw Term B Loan or any Incremental Term Loan first to repay all Revolving Loans outstanding on the date of such Delayed Draw Term B Loan or any Incremental Term Loan and thereafter for funding of Borrower’s working capital and for other general corporate purposes (including Capital Expenditures not made in violation of the terms of this Agreement).

(c) Section 3.2(a) of the Credit Agreement is hereby amended by deleting the reference to “4.00 to 1.00” contained therein and inserting “4.50 to 1.00” in lieu thereof.

(d) Section 3.3(b) of the Credit Agreement is hereby amended by deleting the reference to “3.50 to 1.00” contained therein and inserting “4.00 to 1.00” in lieu thereof.

(e) Each of Sections 4.2, 4.6, 4.7, 4.8, 4.11, 4.12, 4.13, 4.15, 4.17, 4.18, 4.20 and 4.24 of the Credit Agreement are amended to replace all references therein to “Closing Date” with references to “First Amendment Closing Date”.

(f) Section 7.10 of the Credit Agreement is hereby amended and restated in its entirety to read as follows:

Section 7.10 Financial Covenants.

The Loan Parties shall not breach or fail to comply with any of the following financial covenants, each of which shall be calculated in accordance with GAAP consistently applied:

(a) Maximum Capital Expenditures. The Loan Parties and their Subsidiaries on a consolidated basis shall not make Capital Expenditures in any Fiscal Year in an aggregate amount in excess of (i) $18,540,000 with respect to the Fiscal Year ending on or about December 31, 2011, (ii) $22,000,000 with respect to the Fiscal Year ending on or about December 31, 2012, (iii) $24,900,000 with respect to the Fiscal Year ending on or about December 31, 2013, (iv) $27,700,000 with respect to the Fiscal Year ending on or about December 31, 2014, (v) $28,100,000 with respect to the Fiscal Year ending on or about December 31, 2015, and (vi) $13,325,000 with respect to the Fiscal Year ending on or about December 31, 2016. If the Loan Parties and their Subsidiaries do not utilize the entire amount of Capital Expenditures permitted in any Fiscal Year, up to 50% of the amount of Capital Expenditures permitted by this Section 7.10(a) for that Fiscal Year and not utilized (exclusive of any amounts carried over from the prior Fiscal Year) may be utilized in the immediately succeeding Fiscal Year (with Capital Expenditures made by the Loan Parties and their Subsidiaries in such succeeding Fiscal Year applied last to such unutilized amount), provided no amount so carried forward may be expended when an Event of Default exists or would be caused thereby.

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(b) Minimum Fixed Charge Coverage Ratio. The Loan Parties and their Subsidiaries shall have on a consolidated basis, as of the end of each Fiscal Quarter, a Fixed Charge Coverage Ratio, for the four Fiscal Quarters then ended, of not less than the following with respect to the Fiscal Quarter set forth opposite each such ratio below.

(c) Maximum Total Leverage Ratio. The Loan Parties and their Subsidiaries shall have on a consolidated basis as of the end of each Fiscal Quarter, a Total Leverage Ratio for the four Fiscal Quarters then ended, of not more than the following with respect to the Fiscal Quarter set forth opposite each such ratio below:

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; provided, that, after an initial public offering of Stock of Holdings pursuant to an effective registration statement under the Securities Act of 1933, the Loan Parties and their Subsidiaries shall have on a consolidated basis as of the end of each Fiscal Quarter thereafter, a Total Leverage Ratio for the four Fiscal Quarters then ended of not more than the lesser of (i) the applicable ratio with respect to the Fiscal Quarter set forth opposite each such ratio above and (ii) 2.75:1.00.

(d) Maximum Lease Adjusted Leverage Ratio. The Loan Parties and their Subsidiaries shall have on a consolidated basis as of the end of each Fiscal Quarter, a Lease Adjusted Leverage Ratio for the four Fiscal Quarters then ended, of not more than the following with respect to the Fiscal Quarter set forth opposite each such ratio below:

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(g) Schedule 1.1 to the Credit Agreement is hereby amended to add the following defined terms thereto in appropriate alphabetical order:

“First Amendment” shall mean that certain Consent and First Amendment dated as of the First Amendment Closing Date among Borrower, the Guarantors party thereto, the Lenders party thereto and Administrative Agent.

“First Amendment Closing Date” means March 21, 2012.

“Closing Date Term A Loan” shall mean the term loan funded on the Closing Date under the Closing Date Term A Loan Commitment pursuant to Section 2.1(b) (it being understood that such term shall refer to the aggregate Closing Date Term A Loan funded to Borrower when used in the context of all Term A Loan Lenders collectively and a particular Term A Loan Lender’s portion of the aggregate Closing Date Term A Loan when used in the context of an individual Term A Loan Lender).

“Closing Date Term A Loan Commitment” shall mean (a) as to any Lender, the commitment of such Lender to make its Pro Rata Share of the Closing Date Term A Loan as set forth on the applicable signature page to this Agreement on the Closing Date as “Term A Loan Commitment” (as adjusted to reflect any assignments as permitted hereunder) and (b) as to all Lenders, the aggregate commitment of all Lenders to make the Closing Date Term A Loan, which aggregate commitment was Fifty Two Million Five Hundred Thousand and No/100 Dollars ($52,500,000.00) on the Closing Date.

“Proposed Transactions” shall have the meaning assigned to it in the First Amendment.

. “Second Term A Loan” shall mean the term loan funded on the First Amendment Closing Date under the Second Term A Loan Commitment pursuant to Section 2.1(b) (it being understood that such term shall refer to the aggregate Second Term A Loan funded to Borrower when used in the context of all Term A Loan Lenders collectively and a particular Term A Loan Lender’s portion of the aggregate Second Term A Loan when used in the context of an individual Term A Loan Lender).

“Second Term A Loan Commitment” shall mean (a) as to any Lender, the commitment of such Lender to make its Pro Rata Share of the Second Term A Loan as set forth on the applicable signature page to the First Amendment (as adjusted to reflect any assignments as permitted hereunder) and (b) as to all Lenders, the aggregate commitment of all Lenders to make the Second Term A Loan, which aggregate commitment shall be Twenty Five Million and No/100 Dollars ($25,000,000.00) on the First Amendment Closing Date.

(h) The following definitions set forth in Schedule 1.1 to the Credit Agreement are each hereby amended and restated in their entirety to read as follows:

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“Pro Rata Share” shall mean (a) with respect to all matters relating to any Lender with respect to the Revolving Loan, the percentage obtained by dividing (i) the Revolving Loan Commitment of that Lender by (ii) the aggregate Revolving Loan Commitments of all Lenders (provided, after the Revolving Loan Commitments have expired or been terminated, the applicable outstanding balances of the Revolving Loan and Letter of Credit Obligations held by such Lender and all the Lenders, respectively, shall be used in lieu of the Revolving Loan Commitment in both clauses (i) and (ii)), (b) with respect to all matters relating to any Lender with respect to the Term A Loan, the percentage obtained by dividing (i) the Term A Loan Commitment of that Lender by (ii) the aggregate Term A Loan Commitments of all Lenders (provided, after the Closing Date, the applicable outstanding principal balances of the Term A Loan held by such Lender and all Lenders, respectively, shall be used in lieu of the Term A Loan Commitment in both clauses (i) and (ii)), (c) with respect to all matters relating to any Lender with respect to the Closing Date Term A Loan, the percentage obtained by dividing (i) the outstanding principal balance of the Closing Date Term A Loan held by that Lender by (ii) the aggregate outstanding principal balance of the Closing Date Term A Loan held by all Lenders, (d) with respect to all matters relating to any Lender with respect to the Second Term A Loan, the percentage obtained by dividing (i) the Second Term A Loan Commitment of that Lender by (ii) the aggregate Second Term A Loan Commitments of all Lenders (provided, after the First Amendment Closing Date, the applicable outstanding principal balances of the Second Term A Loan held by such Lender and all Lenders, respectively, shall be used in lieu of the Second Term A Loan Commitment in both clauses (i) and (ii)), (e) with respect to all matters relating to any Lender with respect to the Delayed Draw Term B Loan, the percentage obtained by dividing (i) the Delayed Draw Term B Loan Commitment of that Lender by (ii) the aggregate Delayed Draw Term B Loan Commitments of all Lenders (provided, after the Delayed Draw Term B Loan Commitments have expired or been terminated, the applicable outstanding principal balances of the Delayed Draw Term B Loan held by such Lender and all Lenders, respectively, shall be used in lieu of the Delayed Draw Term B Loan Commitment in both clauses (i) and (ii)), (f) with respect to all matters relating to any Lender with respect to the Incremental Term Loan, the percentage obtained by dividing (i) the outstanding principal balance of the Incremental Term Loan held by such Lender by (ii) the aggregate outstanding principal balance of the Incremental Term Loans held by all Lenders, and (g) with respect to any other matters set forth in the Agreement and other Loan Documents, the percentage obtained by dividing (i) the Commitments of that Lender by (ii) the aggregate Commitments of all Lenders (provided, (A) after the Revolving Loan Commitments, and/or Delayed Draw Term B Loan Commitments have expired or been terminated, the applicable outstanding balances of the Revolving Loan and Letter of Credit Obligations, or Delayed Draw Term B Loans, as applicable, held by such Lender and all Lenders, respectively, shall be used in lieu of the Revolving Loan Commitment and/or Delayed Draw Term B Loan Commitments in both clauses (i) and (ii), and (B) after the Closing Date, the applicable outstanding principal balances of the Term A Loan and Incremental Term Loan held by such Lender and all Lenders, respectively, shall be used in lieu of the Term Loan Commitments in both clauses (i) and (ii)), in each case as any such percentages may be adjusted by assignments permitted pursuant to Section 10.1.

“Term A Loan” shall mean, collectively, the Closing Date Term A Loan and the Second Term A Loan (it being understood that such term shall refer to the aggregate Term A Loan funded to Borrower when used in the context of all Term A Loan Lenders collectively and a particular Term A Loan Lender’s portion of the aggregate Term A Loan when used in the context of an individual Term A Loan Lender).

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“Term A Loan Commitment” shall mean (a) as to any Lender, collectively, the Closing Date Term A Loan Commitment of such Lender and the Second Term A Loan Commitment of such Lender and (b) as to all Lenders, collectively, the aggregate Closing Date Term A Loan Commitment of all Lenders and the aggregate Second Term A Loan Commitment of all Lenders.

(i) Exhibit 5.1(b) to the Credit Agreement is hereby amended and restated in its entirety as set forth on the corresponding exhibit attached hereto as Exhibit C.

(j) Schedules 4.6, 4.7, 4.8, 4.13 and 7.3 to the Credit Agreement are hereby amended and restated in their entirety as set forth on the corresponding schedules attached hereto as Exhibit D.

3. Conditions to Effectiveness. The effectiveness of this Amendment is subject to the prior or concurrent consummation of each of the following conditions:

(a) Administrative Agent shall have received a copy of this Amendment executed by Borrower, each Guarantor, Administrative Agent, the Requisite Lenders and each Term A Loan Lender making a Second Term A Loan to Borrower;

(b) Administrative Agent shall have received, on behalf of GE Capital Financial Inc., as a Lender, an Amended and Restated Term A Loan Note executed by Borrower in favor GE Capital Financial Inc. substantially in the form of Exhibit 2.13(b)(i) to the Credit Agreement (the “Amended and Restated Term A Loan Note”);

(c) Administrative Agent shall have received a copy of a Solvency Certificate executed by the Chief Financial Officer or Treasurer of Borrower, stating that the Loan Parties, on a consolidated basis, will be Solvent upon the consummation of the transactions contemplated herein;

(d) Administrative Agent shall have received a copy of resolutions of the Governing Body of Borrower authorizing the execution, delivery and performance of this Amendment, the Distribution, the Termination Payment and the Amended and Restated Term A Loan Note;

(e) Administrative Agent shall have received a copy of resolutions of the Governing Body of Holdings authorizing the execution, delivery and performance of this Amendment and the Redemption;

(f) Administrative Agent shall have received the favorable written opinions of counsel to the Loan Parties in favor of Administrative Agent and the Lenders;

(g) Borrower shall have paid all fees, costs and expenses invoiced, due and payable as of the date hereof under the Credit Agreement and the other Loan Documents; and

(h) no Default or Event of Default shall have occurred and be continuing (including immediately after giving effect to) the transactions contemplated by this Amendment.

4. Representations and Warranties. To induce Administrative Agent and the Requisite Lenders to enter into this Amendment, each Loan Party represents and warrants to Administrative Agent and Lenders:

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(a) that the execution, delivery and performance of this Amendment has been duly authorized by all requisite corporate action on the part of such Loan Party and that this Amendment has been duly executed and delivered by such Loan Party;

(b) this Amendment constitutes the legal, valid and binding obligation of such Loan Party and is enforceable against such Loan Party in accordance with its terms, subject to bankruptcy, insolvency and similar laws affecting the enforceability of creditors’ rights generally and to general principles of equity; and

(c) that each of the representations and warranties of Borrower and each other Loan Party set forth in the Credit Agreement are true and correct in all material respects (except (i) to the extent such representation or warranty contains any materiality qualifier, including references to “material,” “Material Adverse Effect” or dollar thresholds, in which case such representations and warranties are true and correct in any respect and (ii) to the extent stated to relate to a specific earlier date, in which case such representations and warranties are true and correct as of such earlier date).

5. Severability. Any provision of this Amendment held by a court of competent jurisdiction to be invalid or unenforceable shall not impair or invalidate the remainder of this Amendment and the effect thereof shall be confined to the provision so held to be invalid or unenforceable.

6. References. Any reference to the Credit Agreement contained in any document, instrument or Credit Agreement executed in connection with the Credit Agreement shall be deemed to be a reference to the Credit Agreement as modified by this Amendment.

7. Counterparts. This Amendment may be executed in one or more counterparts, each of which shall constitute an original, but all of which taken together shall be one and the same instrument. Receipt by telecopy or electronic mail of any executed signature page to this Amendment shall constitute effective deliver of such signature page.

8. Ratification. The terms and provisions set forth in this Amendment shall modify and supersede all inconsistent terms and provisions of the Credit Agreement and shall not be deemed to be a consent to the modification or waiver of any other term or condition of the Credit Agreement. Except as expressly modified and superseded by this Amendment, the terms and provisions of the Credit Agreement and the other Loan Documents are ratified and confirmed and shall continue in full force and effect.

[Signature Page Follows]

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed under seal and delivered by their respective duly authorized officers on the date first written above.