Exhibit 32.1

Certification of the 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 The Gap, Inc. (the “Company”) on Form 10-Q for the period ended May 1, 2004 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Paul S. Pressler, President and Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. §1350, as adopted pursuant to §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.

/s/ PAUL S. PRESSLER

Paul S. Pressler

President and Chief Executive Officer

May 27, 2004