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                                                                    EXHIBIT 10.6


                                  June 10, 2002

Chiles Offshore Inc.
ATTN: Dick Fagerstal
11200 Richmond, Suite 490
Houston, TX 77082-2618


     Re:    Chiles Offshore Inc. (the "Company")-- Transactions with SEACOR SMIT


Dear Dick:

     This is in response to your letter of June 3, 2002 concerning the captioned
matter. We note your statement regarding the 2002 budgeted projected fee of
$6,422 per month to SEACOR SMIT for the shared aircraft usage and, for the
avoidance of doubt, confirm that said arrangement between Chiles Offshore Inc.
and SEACOR SMIT shall cease upon the Effective Time of the Merger. Additionally,
the Houston office space sublease effective March 1, 2002 between SEACOR Marine
Inc. and Chiles Offshore Inc. shall terminate on the Effective Time of the
Merger. Bringing both of these matters to conclusion upon closing of the Merger
is in accordance with the provisions of Section 2.6 of the May 14, 2002 SEACOR
SMIT Inc. Voting Agreement, which states that there are no contracts or
understandings between SEACOR SMIT or its affiliates and Chiles other than the
specified Related Party Agreements and provides that all such agreements
terminate in their entirety as of the Effective Time of the Merger.

     We concur that these payments were discussed at our negotiations in Houston
but were not disclosed in the Merger Agreement. Your counsel contacted Baker &
McKenzie after the Merger Agreement was signed and asked whether the disclosure
schedules should be amended to reflect the arrangements in respect of the
aircraft usage. Mr. Rabun indicated to Mr. Zeltner that it was not necessary and
acknowledged that ENSCO was aware of the arrangement. Whether the arrangement
needs to be disclosed in the S-4 is a disclosure obligation of Chiles under the
proxy rules. We note that you have elected not to disclose this arrangement in
your previous SEC filings and assume this is the correct decision.

     In sum, we request your acknowledgment that the shared aircraft usage
arrangement between Chiles Offshore Inc. and SEACOR SMIT and the sublease
between SEACOR Marine Inc. and Chiles Offshore Inc. shall cease upon the
Effective Time of the Merger. In addition, we request that you concur that each
of these arrangements will be considered to be a "Related Party Agreement" for
purposes of the Voting Agreement dated as of May 14, 2002 by and between ENSCO
International Incorporated and SEACOR SMIT Inc.




CCG/dmc

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June 10, 2002
Page 2



     Please confirm your acknowledgment of the above by signing where indicated
on the attached copy of this letter and returning the same to the undersigned,
it being acknowledged and agreed by ENSCO that any nondisclosure of the sublease
between Chiles Offshore Inc. and SEACOR Marine Inc. and the aircraft usage
arrangement between Chiles Offshore Inc. and SEACOR SMIT Inc. in the Merger
Agreement or the SEACOR Voting Agreement shall not constitute a violation of the
terms of either said Merger Agreement or said SEACOR Voting Agreement.


                                                       Regards,

                                                       /s/ C. CHRISTOPHER GAUT

                                                       C. Christopher Gaut
                                                       Senior Vice President

cc:      Daniel W. Rabun, Baker & McKenzie
         David E. Zeltner, Weil Gotshal & Manges




Acknowledged and Agreed:

CHILES OFFSHORE INC.



     /s/ DICK FAGERSTAL
     -------------------------------------
By:  Dick Fagerstal
     Senior Vice President, Chief Financial
     Officer and Secretary




CCG/dmc