EXHIBIT 32.1

                                  CERTIFICATION
                       PURSUANT TO 18 U.S.C. SECTION 1350,
           AS ADOPTED BY SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

         I, James S. Tisch, as Chief Executive Officer of Diamond Offshore
Drilling, Inc. (the "Company"), certify, pursuant to 18 U.S.C. Section 1350, as
adopted by Section 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

         (1) the accompanying Form 10-Q report of the Company for the period
ending September 30, 2003, as filed with the U.S. Securities and Exchange
Commission (the "Report"), fully complies with the requirements of Section 13(a)
or 15(d) of the Securities Exchange Act of 1934, as amended; and

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

Dated: November 4, 2003

                                    /s/ James S. Tisch
                                    --------------------------------------------
                                    James S. Tisch,
                                    Chief Executive Officer of the Company