Chuy's (CHUY) 10-Q 2016 Q1 Quarterly report

Exhibit 32.1

CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO SECTION 906 OF

THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q of Chuy’s Holdings, Inc., a Delaware Corporation (the “Company”), for the period ending March 27, 2016, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), the undersigned, Steven J. Hislop, President and Chief Executive Officer of the Company, and Jon W. Howie, Vice President and Chief Financial Officer of the Company, each certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 that:

(1) The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company as of the dates and for the periods indicated.

Date: May 5, 2016

/s/ Steven J. Hislop

Steven J. Hislop

President and Chief Executive Officer

(Principal Executive Officer)

/s/ Jon W. Howie

Jon W. Howie

Vice President and Chief Financial Officer

(Principal Financial Officer)