<PAGE>
                                                                     Exhibit 4.2


                             SUPPLEMENTAL INDENTURE


      SUPPLEMENTAL INDENTURE (this "Supplemental Indenture"), dated as of May
26, 2004, among Arizona Charlie's, LLC (f/k/a Arizona Charlie's, Inc.), a Nevada
limited liability company, Charlie's Holding LLC, a Delaware limited liability
company, Fresca, LLC, a Nevada limited liability company, Stratosphere
Advertising Agency, a Nevada corporation, Stratosphere Corporation, a Delaware
corporation, Stratosphere Development, LLC, a Delaware limited liability
company, Stratosphere Gaming Corp., a Nevada corporation, Stratosphere Land
Corporation, a Nevada corporation, and Stratosphere Leasing, LLC, a Delaware
limited liability company (together, the "Guaranteeing Subsidiaries"), each a
subsidiary of American Casino & Entertainment Properties LLC, a Delaware limited
liability company, as issuer ("ACEP") (or its permitted successor), American
Casino & Entertainment Properties Finance Corp., a Delaware corporation, as
co-issuer ("ACEP Finance", together with ACEP, the "Company") and Wilmington
Trust Company, as trustee under the Indenture referred to below (the "Trustee").

                            W I T N E S S E T H

      WHEREAS, the Company has heretofore executed and delivered to the Trustee
an indenture (the "Indenture"), dated as of January 29, 2004 providing for the
issuance of 7.85% Senior Secured Notes due 2012 (the "Notes");

      WHEREAS, the Indenture provides that under certain circumstances the
Guaranteeing Subsidiaries shall execute and deliver to the Trustee a
supplemental indenture pursuant to which each Guaranteeing Subsidiary shall
unconditionally guarantee all of the Company's Obligations under the Notes and
the Indenture on the terms and conditions set forth herein (the "Note
Guarantee"); and

      WHEREAS, pursuant to Section 9.01 of the Indenture, the Trustee is
authorized to execute and deliver this Supplemental 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 Guaranteeing Subsidiaries mutually covenant and agree for the equal and
ratable benefit of the Holders of the Notes as follows:

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

      2. AGREEMENT TO GUARANTEE. Each Guaranteeing Subsidiary hereby agrees to
be bound by the terms of the Indenture and to unconditionally Guarantee all of
the Company's obligations under the Notes, the Indenture and the Collateral
Documents on the terms set forth in the Indenture and agrees to execute and
deliver a Note Guarantee in the form attached as Exhibit E to the Indenture.

      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
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BUT WITHOUT GIVING EFFECT TO APPLICABLE PRINCIPLES OF CONFLICTS OF LAW TO THE
EXTENT THAT THE APPLICATION OF THE LAWS OF ANOTHER JURISDICTION WOULD BE
REQUIRED THEREBY.

      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.

      6. THE TRUSTEE. The Trustee shall not be responsible in any manner
whatsoever for or in respect of the validity or sufficiency of this Supplemental
Indenture or for or in respect of the recitals contained herein, all of which
recitals are made solely by the Guaranteeing Subsidiaries and the Company.

                  [Remainder of page intentionally left blank.]


                                      -2-
<PAGE>
      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.


                                    AMERICAN CASINO & ENTERTAINMENT
                                    PROPERTIES LLC


                                    By: /s/ Richard P. Brown
                                        ------------------------------------
                                        Name: Richard P. Brown
                                        Title:  President and Chief
                                        Executive Officer


                                    AMERICAN CASINO & ENTERTAINMENT
                                    PROPERTIES FINANCE CORP.


                                    By: /s/ Richard P. Brown
                                        ------------------------------------
                                        Name:  Richard P. Brown
                                        Title:  President and Chief
                                        Executive Officer


                                    CHARLIE'S HOLDING LLC

                                    By:  American Casino & Entertainment
                                         Properties LLC, its sole member

                                         By: /s/ Richard P. Brown
                                             -------------------------------
                                            Name:  Richard P. Brown
                                            Title: President and Chief
                                            Executive Officer


                                    ARIZONA CHARLIE'S, LLC


                                    By: /s/ Denise Barton
                                        ------------------------------------
                                        Name:  Denise Barton
                                        Title:  Senior Vice President,
                                        Chief Financial Officer, Secretary
                                        and Treasurer


                    SIGNATURE PAGE TO SUPPLEMENTAL INDENTURE
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                                    FRESCA, LLC

                                    By: Charlie's Holding LLC, its sole
                                    member

                                        By: American Casino &
                                             Entertainment Properties LLC,
                                             its sole member


                                             By: /s/ Richard P. Brown
                                                 -----------------------------
                                                Name:  Richard P. Brown
                                                Title:  President and
                                                Chief Executive Officer


                                    STRATOSPHERE CORPORATION


                                    By: /s/ Richard P. Brown
                                        ------------------------------------
                                        Name:  Richard P. Brown
                                        Title:  President and Chief
                                        Executive Officer


                                    STRATOSPHERE DEVELOPMENT, LLC

                                    By: Stratosphere Corporation, member


                                       By: /s/ Richard P. Brown
                                           -----------------------------------
                                          Name:  Richard P. Brown
                                          Title:  President and Chief
                                          Executive Officer


                                    By: Arizona Charlie's, LLC, member


                                       By: /s/ Denise Barton
                                           -----------------------------------
                                          Name:  Denise Barton
                                          Title:  Senior Vice President,
                                          Chief Financial Officer,
                                          Secretary and Treasurer


                    SIGNATURE PAGE TO SUPPLEMENTAL INDENTURE
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<PAGE>
                                    By: Fresca, LLC, member

                                       By: Charlie's Holding LLC, its sole
                                              member

                                           By: American Casino &
                                                Entertainment Properties
                                                LLC, its sole member

                                               By: /s/ Richard P. Brown
                                                   ---------------------------
                                                  Name:  Richard P. Brown
                                                  Title: President and
                                                         Chief Executive
                                                         Officer


                                    STRATOSPHERE GAMING CORP.



                                    By: /s/ Richard P. Brown
                                        ------------------------------------
                                          Name:  Richard P. Brown
                                          Title:  President and Chief
                                                  Executive Officer


                                    STRATOSPHERE LEASING, LLC

                                    By: Stratosphere Corporation, its sole
                                    member



                                    By: /s/ Richard P. Brown
                                        ------------------------------------
                                        Name:  Richard P. Brown
                                        Title: President and Chief
                                               Executive Officer


                                    STRATOSPHERE ADVERTISING AGENCY


                                    By: /s/ Denise Barton
                                        ------------------------------------
                                        Name:  Denise Barton
                                        Title:  Chief Financial Officer,
                                                Secretary and Treasurer


                                    STRATOSPHERE LAND CORPORATION


                                    By: /s/ Denise Barton
                                        ------------------------------------
                                        Name:  Denise Barton
                                        Title:  Secretary and Treasurer


                    SIGNATURE PAGE TO SUPPLEMENTAL INDENTURE
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                            WILMINGTON TRUST COMPANY


                               By: /s/ Michael G. Oller, Jr.
                                   ---------------------------------
                                   Name:  Michael G. Oller, Jr.
                                   Title:  Senior Financial
                                           Services Officer


                    SIGNATURE PAGE TO SUPPLEMENTAL INDENTURE
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