POWER OF ATTORNEY

    Know all by these presents, that the undersigned hereby constitutes and appoints each of
Jon W. Howie, Tim Larson and Susan Kittrell or his/her designee, signing singly, the
undersigned's true and lawful attorney-in-fact to:

      (1)    execute for and on behalf of the undersigned, in the undersigned's
capacity as an officer and/or director of Chuy's Holdings, Inc. (the "Company"), Forms 3,
4 and 5 in accordance with Section 16(a) of the Securities Exchange Act of 1934 and the
rules thereunder;

      (2)    do and perform any and all acts for and on behalf of the undersigned
which may be necessary or desirable to complete and execute any such Form 3, 4 or 5,
complete and execute any amendment or amendments thereto, and timely file such form
with the United States Securities and Exchange Commission and any stock exchange or
similar authority; and

      (3)    take any other action of any type whatsoever in connection with the
foregoing which, in the opinion of such attorney-in-fact, may be of benefit to, in the best
interest of, or legally required by, the undersigned, it being understood that the
documents executed by such attorney-in-fact on behalf of the undersigned pursuant to
this Power of Attorney shall be in such form and shall contain such terms and conditions
as such attorney-in-fact may approve in such attorney-in-fact's discretion.

      The undersigned hereby grants to each such attorney-in-fact full power and authority to
do and perform any and every act and thing whatsoever requisite, necessary, or proper to be done
in the exercise of any of the rights and powers herein granted, as fully to all intents and purposes
as the undersigned might or could do if personally present, with full power of substitution or
revocation, hereby ratifying and confirming all that such attorney-in-fact, or such attorney-in-
fact's substitute or substitutes, shall lawfully do or cause to be done by virtue of this Power of
Attorney and the rights and powers herein granted.  The undersigned acknowledges that the
foregoing attorneys-in-fact, in serving in such capacity at the request of the undersigned, are not
assuming, nor is the Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Securities Exchange Act of 1934.

      The execution by the undersigned of this Power of Attorney hereby expressly revokes
and terminates any powers of attorney previously granted by the undersigned relating to Forms 3,
4 and 5 with respect to the undersigned's holdings of and transactions in securities issued by the
Company.  This Power of Attorney shall remain in full force and effect until the undersigned is
no longer required to file Forms 3, 4 and 5 with respect to the undersigned's holdings of and
transactions in securities issued by the Company, unless earlier revoked by the undersigned in a
signed writing delivered to the foregoing attorneys-in-fact.

      IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of September 14, 2018.

                                          /s/ John Mountford
                      ---------------------------------------------
                       Name: John Mountford