Diamond Offshore Drilling (DODRW) 10-Q 2008 Q3 Quarterly report

Exhibit 32.1

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

     Each of the undersigned hereby certifies, pursuant to 18 U.S.C. § 1350, in his capacity as an officer of Diamond Offshore Drilling, Inc. (the “Company”), that, to his knowledge:

     (1) the Company’s Quarterly Report on Form 10-Q for the quarter ended September 30, 2008 as filed with the U.S. Securities and Exchange Commission on the date hereof (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: October 28, 2008

\s\ Lawrence R. Dickerson                              
Lawrence R. Dickerson
Chief Executive Officer of the Company

\s\ Gary T. Krenek                                        
Gary T. Krenek
Chief Financial Officer of the Company