Exhibit 10.34


                                   ASSIGNMENT

         This Assignment (the "Assignment") entered into on the 31st day of
October, 2001, by and between Chiles Offshore Inc. (formerly Chiles Offshore
LLC), a company organized under the laws of the State of Delaware, ("Chiles")
and Chiles Galileo LLC, a company organized under the laws of the State of
Delaware and a wholly-owned subsidiary of Chiles ("Galileo").


         WHEREAS, Chiles and AMFELS, Inc., a corporation organized under the
laws of the State of Texas, ("Builder") entered into that certain contract dated
April 6, 2000 for the construction by Builder and purchase by Chiles of one
mobile, self-contained and self-elevating 475' leg length platform, as amended
by Amendment No. 1 dated of even date herewith, the (said contract, as amended,
the "Construction Contract").

         WHEREAS, under Article 19 of the Construction Contract, Builder has
consented to the assignment of the Construction Contract by Chiles to a
wholly-owned subsidiary of Chiles, provided that Chiles shall remain primarily
liable for the full and timely performance by such assignee of the obligations
of such assignee under the Construction Contract.

         WHEREAS, Chiles wishes to assign the Construction Contract to Galileo
and Galileo wishes to accept such assignment.

         NOW THEREFORE, in consideration of the foregoing and other good an
valuable consideration:

         1. Chiles does hereby assign all of its right, tittle and interest in,
            under and to the Construction Contract to Galileo.

         2. Galileo does hereby accept such assignment of the Construction
            Contract and agrees to perform all of the obligations of the Owner
            thereunder.

         3. Nothing herein shall supersede the provisions of Section 15 of
            Amendment No. 1 to the Construction Contract.

                            [SIGNATURE PAGE FOLLOWS]




         IN WITNESS WHEREOF, the parties have caused this Assignment to be
executed on their behalf by their respective duly authorized representatives on
the date first shown above.

         CHILES OFFSHORE INC.                     CHILES GALILEO LLC



         By:  /s/ Dick Fagerstal                  By:/s/ Dick Fagerstal

         Name:  Dick Fagerstal                    Name: Dick Fagerstal

         Title:   Senior Vice President           Title:   Senior Vice President

         AMFELS, Inc. hereby consents to said assignment on the condition that
Chiles shall remain primarily liable for the full and timely performance by
Galileo of the obligations of Galileo under the Construction Contract.

         AMFES, INC.



         By:  /s/ Eric Phau

         Title: VP Commercial