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                                                                    EXHIBIT 4.55

                             SUPPLEMENTAL INDENTURE

         Supplemental Indenture (this "Supplemental Indenture"), dated as of
December 1, 1999, between Horseshoe Gaming Holding Corp., a Delaware corporation
(the "Company"), the successor of Horseshoe Gaming, L.L.C. ("LLC"), to the
Indenture referred to below, and U.S. Trust Company of Texas, N.A. (the
"Trustee").

                               W I T N E S S E T H

         WHEREAS, LLC has heretofore executed and delivered to the Trustee an
indenture (the "Indenture"), dated as of June 15, 1997, among LLC, Robinson
Property Group, Limited Partnership and the Trustee providing for the issuance
of 9_% Senior Subordinated Notes due 2007 (the "Notes");

         WHEREAS, LLC and the Company entered into an Agreement of Merger (the
"Merger"), dated as of December 1, 1999, which provides, among other things, for
the merger of LLC with and into the Company;

         WHEREAS, the Indenture permits the Merger to occur if certain
conditions are met and if the Company and the Trustee enter into this
Supplemental Indenture to which the Company expressly assumes from LLC all of
the Obligations of LLC with respect to the Notes and the Indenture.

         NOW, THEREFORE, in consideration of the foregoing and for other good
and valuable consideration, the receipt of which is hereby acknowledged, the
Company and the Trustee mutually covenant and agree as follows:

         1. Capitalized Terms. Capitalized terms used herein without definition
shall have the meanings assigned to them in the Indenture.

         2. Assumption and Discharge. As of the date hereof, the Company
expressly assumes all of the Obligations of LLC with respect to the Notes and
the Indenture, and the parties release LLC from its obligations under the
Indenture and the Notes except as to any obligations that arise from or result
from the Merger.

         THE TERMS OF ARTICLE V OF THE INDENTURE ARE INCORPORATED HEREIN BY
REFERENCE.


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         3. NEW YORK LAW TO GOVERN. THE INTERNAL LAW OF THE STATE OF NEW YORK
SHALL GOVERN AND BE USED TO CONSTRUE THIS SUPPLEMENTAL INDENTURE, INCLUDING,
WITHOUT LIMITATION, SECTION 5-1401 OF THE NEW YORK GENERAL OBLIGATIONS LAW.

         4. Counterparts. The parties may sign any number of copies of this
Supplemental Indenture. Each signed copy shall be an original, but all of them
together represent the same agreement.

         5. Effect of Headings. The Section headings herein are for convenience
only and shall not affect the construction hereof.

         IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture to be duly executed and attested, all as of the date first above
written.

                                    THE COMPANY:

                                    HORSESHOE GAMING HOLDING CORP.

                                    By:
                                        ------------------------------------
                                        Name: Jack B. Binion
                                        Title:   President


                                    TRUSTEE:

                                    U.S. TRUST COMPANY OF TEXAS, N.A.


                                    By:
                                        ------------------------------------
                                        Name:
                                        Title:


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