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 Annual Report of AutoZone, Inc. (the "Company") on Form
10-K for the fiscal year ended August 28, 2004, as filed with the Securities and
Exchange Commission on the date hereof (the "Report"), I, Steve Odland,
Chairman, President and Chief Executive Officer of the Company, certify,
pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the
Sarbanes-Oxley Act of 2002, that:

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

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



October 27, 2004

                                            /s/ STEVE ODLAND
                                            ----------------------------------
                                            Steve Odland
                                            Chairman, President and
                                            Chief Executive Officer