<PAGE>
 
                                                                 EXHIBIT 4(a)(6)

                                                                [CONFORMED COPY]
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                                  TENNECO INC.


                                      AND


                            THE CHASE MANHATTAN BANK
                            (National Association),

                                                                      As Trustee



                                  ----------



                         Eighth Supplemental Indenture

                          Dated as of October 1, 1992

                                       TO

                                   Indenture

                          Dated as of March 15, 1988


                                  ----------


                         Providing for the issuance of

                              7-7/8% Notes due 2002



================================================================================
<PAGE>
 
EIGHTH SUPPLEMENTAL INDENTURE dated as of October 1, 1992 between TENNECO INC.,
a corporation duly organized and existing under the laws of the State of
Delaware (hereinafter called the "Company"), and THE CHASE MANHATTAN BANK
(National Association), a national banking association existing under the laws
of the United States of America, as trustee (hereinafter called the "Trustee").

   WHEREAS, the Company has heretofore executed and delivered to the Trustee an
indenture dated as of March 15, 1988 (hereinafter called the "Original
Indenture"), to provide for the issue of an unlimited amount of debentures,
notes and/or other debt obligations of the Company (hereinafter referred to as
the "Securities"), the terms of which are to be determined as set forth in (S)
2.02 of the Original Indenture; and

   WHEREAS, (S)12.01 of the Original Indenture provides, among other things,
that the Company and the Trustee may enter into indentures supplemental to the
Original Indenture for, among other things, the purpose of setting forth the
terms of Securities of any series; and

   WHEREAS, the Company desires to create a series of the Securities in an
aggregate principal amount of $500,000,000 to be designated the "7-7/8% Notes
due 2002" (the "Notes"), and all action on the part of the Company necessary to
authorize the issuance of the Notes under the Original Indenture and this Eighth
Supplemental Indenture has been duly taken; and

   WHEREAS, all acts and things necessary to make the Notes, when executed by
the Company and authenticated and delivered by the Trustee as in the Indenture
provided, the valid and binding obligations of the Company, and to constitute
these presents a valid and binding supplemental indenture and agreement
according to its terms, have been done and performed;

   NOW, THEREFORE, in consideration of the premises and of the mutual covenants
herein contained, and of the acceptance of this trust by the Trustee, and of the
sum of one dollar to the Company duly paid by the Trustee at the execution and
delivery of these presents, and of other valuable consideration the receipt
whereof is hereby acknowledged and in order to authorize the authentication and
delivery of and to set forth the terms of the Notes,
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                                       2

   IT IS HEREBY COVENANTED, DECLARED AND AGREED by and between the parties
hereto, for the benefit of holders of the Notes issued under the Indenture, as
follows:

                                  ARTICLE I.

                  TERMS AND ISSUANCE OF 7-7/8% NOTES DUE 2002

   (S)1.01. Issue of Notes. A series of Securities which shall be designated the
"7-7/8% Notes due 2002" shall be executed, authenticated and delivered in
accordance with the provisions of, and shall in all respects be subject to, the
terms, conditions and covenants of the Indenture, including without limitation
the terms set forth in this Eighth Supplemental Indenture (including the form of
Notes set forth in (S)1.02 hereof). The aggregate principal amount of Notes
which may be authenticated and delivered under the Indenture shall not, except
as permitted by the provisions of (S)(S)2.07, 2.08, 2.10, 2.11 or 3.02 of the
Indenture, exceed $500,000,000. The entire amount of Notes may forthwith be
executed by the Company and delivered to the Trustee and shall be authenticated
by the Trustee and delivered to or upon the order of the Company pursuant to (S)
2.03 of the Indenture.

   (S)1.02. Forms of Notes and Authentication Certificate. The forms of the
Notes and the Trustee's certificate of authentication shall be substantially as
follows:
                             [FORM OF FACE OF NOTE]
                                  TENNECO INC.

                             7-7/8% NOTE DUE 2002

No.                                                                  $

   Tenneco Inc., a corporation organized and existing under the laws of the
State of Delaware (hereinafter called the "Company," which term shall include
any successor corporation as defined in the Indenture hereinafter referred to),
for value received, hereby promises to pay to     or registered assigns, the sum
of     Dollars on October 1, 2002, in any coin or currency of the United States
of America which at the time of payment is legal tender for the payment of
public and private debts, and to pay
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                                       3

to the registered holder hereof as hereinafter provided interest thereon at the
rate per annum specified in the title hereof in like coin or currency, from the
April 1 or October 1 next preceding the date hereof to which interest has been
paid, unless the date hereof is a April 1 or October 1 to which interest on the
Notes has been paid, in which case from the date hereof, or unless no interest
has been paid on the Notes since the original issue date (hereinafter referred
to) of this Note, in which case from the original issue date, semi-annually on
April 1 and October 1 in each year, until payment of said principal sum has been
made or duly provided for, and to pay interest on any overdue principal and (to
the extent permitted by law) on any overdue installment of interest at the rate
of 7-7/8% per annum. Notwithstanding the foregoing, when there is no existing
default in the payment of interest on the Notes, if the date hereof is after
March 16 or September 16 and prior to the following April 1 or October 1, as the
case may be, this Note shall bear interest from such April 1 or October 1;
provided, however, that if the Company shall default in the payment of interest
due on such April 1 or October 1, then this Note shall bear interest from the
April 1 or October 1 to which interest has been paid or, if no interest has been
paid on the Notes since the original issue date of this Note, from the original
issue date. The interest so payable on any April 1 or October 1 will, subject to
certain exceptions provided in the Indenture hereinafter referred to, be paid to
the person in whose name this Note is registered at the close of business on the
March 16 or September 16, as the case may be, next preceding such April 1 or
October 1, or if such March 16 or September 16 is not a business day, the
business day next preceding such March 16 or September 16. Interest on this Note
shall be computed on the basis of a 360-day year of twelve 30-day months. Both
principal of and interest on this Note are payable at the principal office of
the Trustee in the Borough of Manhattan, The City of New York, New York;
provided, however, that payment of interest may be made, at the option of the
Company, by check mailed to the address of the person entitled thereto as such
address shall appear on the Note register. The original issue date in respect of
the Notes is October 1, 1992.

   ADDITIONAL PROVISIONS OF THIS NOTE ARE CONTAINED ON THE REVERSE HEREOF AND
SUCH PROVISIONS SHALL FOR ALL PURPOSES HAVE THE SAME EFFECT AS THOUGH FULLY SET
FORTH AT THIS PLACE.
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                                       4

   This Note shall not be entitled to any benefit under the Indenture
hereinafter referred to, or become valid or obligatory for any purpose, until
the Trustee under the Indenture shall have signed the form of certificate of
authentication endorsed hereon.

   In Witness Whereof, Tenneco Inc. has caused this Instrument to be signed in
its name by its Chairman of the Board or its President or a Vice President, and
its corporate seal (or a facsimile thereof) to be hereto affixed and attested by
its Secretary or an Assistant Secretary.

Dated
     -----------------------------

                                       Tenneco Inc.


                                       By
                                         -----------------------------------
                                                       Chairman of the Board

Attest:




----------------------------------
                         Secretary


                           [FORM OF REVERSE OF NOTE]

                                 TENNECO INC.

                             7-7/8% NOTE DUE 2002

   This Note is one of a duly authorized issue of Notes of the Company known as
its 7-7/8% Notes due 2002 (herein called the "Notes"), limited to the aggregate
principal amount of $500,000,000, all issued under and equally entitled to the
benefits of an Indenture (herein, together with any amendments and supplements
thereto, including without limitation the form and terms of

<PAGE>
 
                                       5

Securities issued pursuant thereto, called the "Indenture"), dated as of March
15, 1988, executed by the Company to The Chase Manhattan Bank (National
Association) (herein, together with any successor thereto, called the
"Trustee"), as Trustee, to which Indenture reference is hereby made for a
statement of the rights thereunder of the Trustee and of the registered holders
of the Notes and of the duties thereunder of the Trustee and the Company.

   The Notes are not subject to redemption prior to maturity.

   The Indenture permits the Company to issue unsecured debentures, notes and/or
other evidences of indebtedness in one or more series ("Securities") up to such
principal amount or amounts as may be authorized in accordance with the terms of
the Indenture.

   To the extent permitted by, and as provided in, the Indenture, modifications
or alterations of the Indenture and of the rights and obligations of the Company
and of the holders of the Notes may be made with the consent of the Company and
with the consent of the holders of not less than a majority in principal amount
of the Securities of all series then outstanding under the Indenture (treated as
a single class) which are affected by the modification or amendment thereto;
provided, however, that without the consent of the holder hereof no such
modification or alteration shall be made which will affect the terms of payment
of the principal of or interest on this Note.

   In case a default, as defined in the Indenture, shall occur, the principal of
all the Notes at any such time outstanding under the Indenture may be declared
or may become due and payable, upon the conditions and in the manner and with
the effect provided in the Indenture. The Indenture provides that such
declaration may in certain events be waived by the holders of a majority in
principal amount of the Notes outstanding in the case of payment defaults on the
Notes and in certain other events by the holders of a majority in principal
amount of the Securities of all series then outstanding under the Indenture
(treated as a single class) which are affected thereby.

   The Indenture provides that no holder of any Note may enforce any remedy
under the Indenture except in the case of refusal or neglect of the Trustee to
act after notice of default and after request by the holders of a majority in
principal amount of the outstanding Notes in certain events (and in certain
other events by the holders of a majority in principal amount of the Securities
of all series then outstanding under the Indenture, treated as a single
<PAGE>
 
                                       6

class, which are affected thereby) and the offer to the Trustee of security and
indemnity satisfactory to it; provided, however, that such provision shall not
prevent the holder hereof from enforcing payment of the principal of or interest
on this Note.

   The transfer of this Note is registrable by the registered holder hereof, in
person or by duly authorized attorney, at the agency of the Company in the
Borough of Manhattan, The City of New York, New York, on books of the Company to
be kept for that purpose at said agency, upon surrender and cancellation of this
Note and on presentation of a duly executed written instrument of transfer, and
thereupon a new Note or Notes, of the same aggregate principal amount and in
authorized denominations, will be issued to the transferee or transferees in
exchange herefor; and this Note, with or without other Notes, may in like manner
be exchanged for one or more new Notes of other authorized denominations but of
the same aggregate principal amount; all subject to the terms and conditions set
forth in the Indenture.

   The Company, the Trustee, any paying agent and any Registrar of the Notes may
deem and treat the person in whose name this Note is registered as the absolute
owner hereof for all purposes whatsoever, and neither the Company nor the
Trustee nor any paying agent nor any Registrar of the Notes shall be affected by
any notice to the contrary.

   No recourse shall be had for the payment of the principal of, or the interest
on, this Note, or for any claim based hereon or on the Indenture, against any
incorporator, or against any stockholder, director or officer, as such, past,
present or future, of the Company, or of any predecessor or successor
corporation, either directly or through the Company or any such predecessor or
successor corporation, whether by virtue of any constitution, statute or rule of
law, or by the enforcement of any assessment or penalty or otherwise, all such
liability, whether at common law, in equity, by any constitution, statute or
otherwise, of incorporators, stockholders, directors or officers being released
by every owner hereof by the acceptance of this Note and as part of the
consideration for the issue hereof, and being likewise released by the terms of
the Indenture; provided, however, that nothing herein or in the Indenture
contained shall be taken to prevent recourse to and the enforcement of the
liability, if any, of any stockholder or subscriber to capital stock of the
Company upon or in respect of shares of capital stock not fully paid up.
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                                       7

   All terms used in this Note which are defined in the Indenture shall have the
meanings assigned to them in the Indenture.

               [FORM OF TRUSTEE'S CERTIFICATE OF AUTHENTICATION]

   This Note is one of the 7-7/8% Notes due 2002 described in the within-
mentioned Indenture.

                                       THE CHASE MANHATTAN BANK
                                        (National Association),

                                                                        Trustee,



                                       By 
                                         --------------------------------------
                                                  Authorized Officer.
<PAGE>
 
                                       8

                                   ARTICLE 2.

                                 MISCELLANEOUS

   (S) 2.01. Execution as Supplemental Indenture. This Eighth Supplemental
Indenture is executed and shall be construed as an indenture supplemental to the
Original Indenture and, as provided in the Original Indenture, this Eighth
Supplemental Indenture forms a part thereof. Except as herein expressly
otherwise defined, the use of the terms and expressions herein is in accordance
with the definitions, uses and constructions contained in the Original
Indenture.

   (S) 2.02. Responsibility for Recitals, Etc. The recitals herein and in the
Notes (except in the Trustee's certificate of authentication) shall be taken as
the statements of the Company, and the Trustee assumes no responsibility for the
correctness thereof. The Trustee makes no representations as to the validity or
sufficiency of this Eighth Supplemental Indenture or of the Notes. The Trustee
shall not be accountable for the use or application by the Company of the Notes
or of the proceeds thereof.

   (S) 2.03. Provisions Binding on Company's Successors. All the covenants,
stipulations, promises and agreements in this Eighth Supplemental Indenture
contained by the Company shall bind its successors and assigns whether so
expressed or not.

   (S) 2.04. New York Contract. This Eighth Supplemental Indenture and each Note
shall be deemed to be a contract made under the laws of the State of New York,
and for all purposes shall be construed in accordance with the laws of said
state.

   (S) 2.05. Execution and Counterparts. This Eighth Supplemental Indenture may
be executed in any number of counterparts, each of which shall be an original
but such counterparts shall together constitute but one and the same instrument.
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                                       9

   IN WITNESS WHEREOF, said TENNECO INC. has caused this Eighth Supplemental
Indenture to be executed in its corporate name by its Chairman of the Board or
its President or one of its Vice Presidents, and said THE CHASE MANHATTAN BANK
(National Association) has caused this Eighth Supplemental Indenture to be
executed in its corporate name by one of its Vice Presidents as of October 1,
1992.

                                       TENNECO INC.



                                       By           E. J. MILAN
                                         -----------------------------------
                                                  Vice President


                                       THE CHASE MANHATTAN BANK 
                                        (National Association)



                                       By          ANN L. EDMONDS
                                         -----------------------------------
                                                   Vice President