<PAGE>
 
                                                                     EXHIBIT 4.2
                            SUPPLEMENTAL INDENTURE


     SUPPLEMENTAL INDENTURE, dated as of May 14, 1998, among Plitt Theatres,
Inc., as Issuer (the "Issuer"), Loews Cineplex Entertainment Corporation, as
Guarantor ("Loews Cineplex") and The Bank of New York, as Trustee (the
"Trustee").

     WHEREAS, the Issuer and Cineplex Odeon Corporation, as Guarantor ("Cineplex
Odeon"), have executed and delivered to the Trustee an Indenture, dated as of
June 23, 1994 (the "Indenture"), providing for the issuance by the Issuer of
$200 million in aggregate principal amount of 10 7/8% Senior Subordinated
Securities (the "Notes") (capitalized terms used but not otherwise defined
herein shall have the meanings assigned to them in the Indenture);

     WHEREAS, pursuant to Section 5.01 of the Indenture, Loews Cineplex will
assume the obligations of Cineplex Odeon as Guarantor of the Notes pursuant to
the terms of the Indenture and the Notes, and Cineplex Odeon will be released
from such obligations;

     NOW, THEREFORE, in consideration of the premises, Loews Cineplex hereby
covenants and agrees with the Trustee and its successor or successors in said
trust under the Indenture as follows:

     Section 1.  Assumption of Obligations.  Loews Cineplex hereby agrees to
                 -------------------------                                  
assume the obligations of Cineplex Odeon as Guarantor under the Parent Guarantee
set forth on Article Twelve of the Indenture for the equal and ratable benefit
of the holders of the Notes, subject to the provisions of Article Thirteen of
the Indenture.

     Section 2.  Notice.  Notices to Loews Cineplex under the Indenture should
                 ------                                                       
be sent to Loews Cineplex Entertainment Corporation, 711 Fifth Avenue, 11th
Floor, New York, New York  10022, Attention: John C. McBride, Jr., General
Counsel, with a copy to Fried, Frank, Harris, Shriver & Jacobson, One New York
Plaza, New York, New York  10004, Attention:  David C. Golay.

     Section 3.  Release.  The Trustee, on behalf of any and all holders of the
                 -------                                                       
Notes, hereby acknowledges, releases and discharges Cineplex Odeon and its
successors and assigns (other than Loews Cineplex), from all obligations owed by
Cineplex Odeon to any and all holders of the Notes arising with respect to the
Parent Guarantee or the Indenture.

     Section 4.  Miscellaneous.
                 ------------- 

<PAGE>
 
     a)  The Indenture as amended and supplemented by this Supplemental
Indenture is in all respects preserved and confirmed.

     b)  This Supplemental Indenture shall form a part of the Indenture for all
purposes, and every holder of the Notes heretofore or hereafter authenticated
and delivered shall be bound hereby.

     c)  For all purposes of this Supplemental Indenture, except as otherwise
defined or unless the context otherwise requires, capitalized terms used in this
Supplemental Indenture and defined in the Indenture shall have the meanings
specified in the Indenture.

     d)  This Supplemental Indenture shall be governed by, and construed in
accordance with, the laws of the State of New York 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.

     e)  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.

                                      -2-

<PAGE>
 
     IN WITNESS WHEREOF, the parties have caused this Supplemental Indenture to
be duly executed as of the date first written above.


                                    PLITT THEATRES, INC.,
                                    as Issuer


                                    By:   /s/ Michael Herman
                                          ---------------------------------
                                          Name:  Michael Herman             
                                          Title: Executive Vice President,  
                                                 Corporate Affairs and      
                                                 Secretary                   


                                    LOEWS CINEPLEX
                                    ENTERTAINMENT CORPORATION,
                                    as Guarantor


                                    By:   /s/ Joseph Sparacio
                                          ----------------------------------
                                          Name:  Joseph Sparacio         
                                          Title: Vice President and    
                                                 Controller 


                                    THE BANK OF NEW YORK,
                                    as Trustee


                                    By:   /s/ Marie E. Trimboli
                                          ---------------------------------
                                          Name:  Marie E. Trimboli   
                                          Title: Assistant Treasurer 

                                      -3-