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                                                                    EXHIBIT 10.5


                                 May 15, 2002



ENSCO International Incorporated
Attn.:  C. Christopher Gaut
2700 Fountain Place
1445 Ross Avenue
Dallas, Texas  75202


Ladies and Gentlemen:

      Reference is made to that certain Merger Agreement (the "Agreement") dated
May 14, 2002 by and among ENSCO International Incorporated ("Parent"), Chore
Acquisition, Inc. ("Merger Sub"), and Chiles Offshore Inc. ("Company"), pursuant
to which Company will become a wholly-owned subsidiary of Parent (the "Merger").
Capitalized terms not defined herein have the meaning given to such terms in the
Agreement. Section 5.7(b) of the Agreement provides, among others, that in
connection with the Merger Company shall terminate (a) that certain Commission
Agreement dated April 1, 2000 by and between Bassoe Offshore (USA), Inc.
("Bassoe") and Company, (b) that certain Commission Agreement (the
"Bassoe-SEACOR Commission Agreement") dated April 1, 2000 among Bassoe, SEACOR
SMIT Inc. ("SEACOR") and Company, (c) that certain Brokerage Arrangement dated
August 5, 1997 between Bassoe Rig Partners Ltd. ("Bassoe Rig") and Company and
(d) that certain Brokerage and Commission Agreement dated December 20, 2001 (the
"Bassoe Commission Agreement") by and between Bassoe and Company (including any
and all other agreements among Bassoe, Bassoe Rig (and their affiliates) and
Company, collectively, the "Related Party Agreements"), with termination to be
effective as of the Effective Time. In order to induce Parent and Merger Sub to
enter into the Agreement and to consummate the Contemplated Transactions, the
undersigned hereby agree that each of the respective Related Party Agreements to
which they are a party shall be terminated in their entirety as of the Effective
Time. The undersigned hereby represent and warrant to Parent that neither the
undersigned nor any of their respective affiliates is a party to any Contract
with any Acquired Company other than the Related Party Agreements. The
undersigned hereby waive any provisions in the Related Party Agreements
requiring prior notice of termination and agree that none of the Acquired
Companies shall incur any Liability as a result of such termination.
Notwithstanding anything to the contrary herein, in accordance with Section 1 of
the Bassoe-SEACOR Commission Agreement, Parent shall pay to Bassoe (a) an amount
equal to $437,500 at the Effective Time in conjunction with the termination of
the Bassoe Commission Agreement and (b) an amount equal to $250,000 within 60
days after delivery of the Vessel to Company by Builder, in accordance with, and
in the manner contemplated by, Section 1 of the Bassoe-SEACOR Commission
Agreement. For the purpose of this letter agreement, "Vessel" and "Builder" have
the meanings assigned to those terms in the Bassoe-SEACOR Commission Agreement.
Except as expressly set forth in this letter agreement, Parent and the Acquired
Companies and their affiliates shall have no Liability (monetary or otherwise)
to Bassoe, Bassoe Rig or any of their affiliates at or following the Effective
Time.
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ENSCO International Incorporated
May 15, 2002
Page 2



      This letter agreement and the rights and obligations of the parties
hereunder shall be construed in accordance with and be governed by the laws of
the State of Delaware (without giving effect to the conflict of law provisions
thereof). All actions and Proceedings arising out of or relating to this letter
agreement must be brought in the courts of the State of Delaware, County of New
Castle, or, if it has or can acquire jurisdiction, in the United States District
Court for the District of Delaware, and each of the undersigned irrevocably
consents to the exclusive jurisdiction of such court in any such Proceeding and
waives any objection to venue therein. This letter agreement may be executed in
multiple counterparts, each of which shall be deemed an original but together
shall constitute one and the same agreement.

                                          Very truly yours,

                                          BASSOE OFFSHORE (USA), INC.


                                          By: /s/ Jonathan Fairbanks
                                              ---------------------------------
                                          Name: Jonathan Fairbanks
                                          Title: President

                                          BASSOE RIG PARTNERS LTD.


                                          By: /s/ Jonathan Fairbanks
                                              ---------------------------------
                                          Name: Jonathan Fairbanks
                                          Title: President

Acknowledged and Accepted this            Acknowledged and Accepted this
16th day of May, 2002                     16th day of May, 2002

ENSCO INTERNATIONAL INCORPORATED          CHILES OFFSHORE INC.



By: /s/ C. C. Gaut                        By: /s/ William E. Chiles
    ----------------------------              ---------------------------------
Name: C. Christopher Gaut                 Name: William E. Chiles
Title: Sr. Vice President                 Title: President