EXHIBIT 32.1

Certification of Chief Executive Officer 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 of Ross Stores, Inc. (the “Company”) on Form 10-Q for the quarter ended October 28, 2017 as filed with the Securities and Exchange Commission on the date hereof (the "Report"), I, Barbara Rentler, as Chief Executive Officer of the Company, hereby certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (“Section 906”), that, to the best of my knowledge:

(1) The Report fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934 (15 U.S.C. 78m); and

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

Date:	December 6, 2017	/s/Barbara Rentler
		Barbara Rentler
		Chief Executive Officer