<PAGE>   1
                                                                  EXHIBIT 10.23


                         THIRD AMENDMENT TO AMENDED AND
                           RESTATED CREDIT AGREEMENT


         This THIRD AMENDMENT AND SUPPLEMENT TO AMENDED AND RESTATED CREDIT
AGREEMENT (this "Third Amendment") executed effective as of December 9, 1999
(the "Effective Date"), is by and among THE HOUSTON EXPLORATION COMPANY, a
Delaware corporation ("Company"); CHASE BANK OF TEXAS, NATIONAL ASSOCIATION (in
its individual capacity, "Chase"), as agent (in such capacity, "Agent") for
each of the lenders that is a signatory hereto or which becomes a signatory
hereto and to the hereinafter described Credit Agreement as provided in Section
12.06 of the Credit Agreement (individually, together with its successors and
assigns, "Lender" and collectively, "Lenders").


                                R E C I T A L S

         A. The Company, the Agent and the Lenders (other than the hereinafter
defined "Additional Lenders") are parties to that certain Amended and Restated
Credit Agreement dated as of March 30, 1999 (said Amended and Restated Credit
Agreement, as amended and supplemented by First Amendment to Amended and
Restated Credit Agreement dated as of May 4, 1999, and as further amended by
Second Amendment to Amended and Restated Credit Agreement dated as of October
6, 1999, "Credit Agreement"), pursuant to which the Lenders agreed to make
loans and issue Letters of Credit to and for the account of the Company.

         B.       The Company, the Lenders and the Agent mutually desire to
amend certain aspects of the Credit Agreement relating to, among other things,
the Borrowing Base and Threshold Amount.

         C.       In view of the foregoing, the Company, the Agent and the
Lenders hereby agree to amend the Credit Agreement in the particulars
hereinafter provided.

         NOW, THEREFORE, in consideration of the premises and other good and
valuable consideration and the mutual benefits, covenants and agreements herein
expressed, the parties hereto now agree as follows:

         Section 1. Certain Terms. All capitalized terms used in this Third
Amendment and not otherwise defined herein shall have the meanings ascribed to
such terms in the Credit Agreement.

         Section 2.  Amendments and Supplements to Credit Agreement.  The
Credit Agreement is hereby amended and supplemented as follows:

                  2.1  Definitions.

                  (a) The following terms defined in Section 1.02 of the Credit
         Agreement are hereby amended as follows:

<PAGE>   2
                           (i)  The term "Agreement" is hereby amended in its
                  entirety to read as follows:

                           "Agreement" shall mean this Credit Agreement, as
                  amended by the First Amendment, as further amended by the
                  Second Amendment, as further amended by the Third Amendment,
                  and as the same may be further amended or supplemented from
                  time to time.

                           (ii) The term "Applicable Margin" is hereby amended
                  in its entirety to read as follows:

         "Applicable Margin" shall mean at the time of calculation, with
respect to any Loan, calculated as a function of the type of such Loan, the
following rate per annum as applicable:

<TABLE>
<CAPTION>
--------------------------------------------------------------------------------------------
   THRESHOLD AMOUNT                FIXED RATE LOAN APPLICABLE      BASE RATE LOAN APPLICABLE
     UTILIZATION                       MARGIN PERCENTAGE              MARGIN PERCENTAGE
--------------------------------------------------------------------------------------------
<S>                                <C>                             <C>
Less than 33%                               0.875%                           0%
Greater than or equal to 33%                1.125%                           0%
but less than 66%
Greater than or equal to 66%                1.375%                           0%
but less than 100%
Greater than or equal to                    1.625%                           0%
100%
--------------------------------------------------------------------------------------------
</TABLE>

                           (iii) The Term "Threshold Amount" is hereby amended
                  in its entirety to read as follows:

                                    "Threshold Amount" shall mean (i) during
                           the period from and including the Effective Date of
                           the Third Amendment to and including the date of the
                           redetermination by the Agent and the Lenders of the
                           Threshold Amount scheduled to occur March 1, 2000,
                           an amount equal to $175,000,000, (ii) during the
                           period from and including March 2, 2000 to and
                           including September 1, 2000, an amount equal to the
                           amount of the March 1, 2000 redetermined Threshold
                           Amount, and (iii) thereafter, the amount equal to
                           the Borrowing Base in effect from time to time. The
                           redetermination of the Threshold Amount on March 1,
                           2000, shall be made using the same criteria used by
                           the Agent and the Lenders prior to the Closing Date
                           to determine the Threshold Amount.

                  (b) Section 1.02 of the Credit Agreement is hereby
         supplemented, where alphabetically appropriate, with the addition of
         the following definition:

                                      -2-

<PAGE>   3
                           "Third Amendment" shall mean that certain Third
                  Amendment to Amended and Restated Credit Agreement dated
                  effective as of December 9, 1999, between the Company, the
                  Agent and the Lenders.

                  2.2  Fees.  Section 2.04 of the Credit Agreement is hereby
          amended as follows:

         (a)      The table found in Section 2.04(a)(i) is hereby amended in
its entirety to read as follows:

------------------------------------------------------------------------------
          THRESHOLD AMOUNT
            UTILIZATION                                 COMMITMENT FEE
------------------------------------------------------------------------------
Less than 33%                                               0.25%
Greater than or equal to 33% but less than 66%              0.30%
Greater than or equal to 66% but less than 100%             0.30%
Greater than or equal to 100%                               0.375%

         (b)      The table found in Section 2.04(b) is hereby amended in its
entirety to read as follows:

------------------------------------------------------------------------------
                 THRESHOLD AMOUNT
                    UTILIZATION                         ISSUANCE FEE
------------------------------------------------------------------------------
Less than 33%                                              0.875%
Greater than or equal to 33% but less                      1.125%
than 66%
Greater than or equal to 66% but less                      1.375%
than 100%
Greater than or equal to 100%                              1.625%
------------------------------------------------------------------------------

                  2.3 Prepayments. Section 2.08(b) of the Credit Agreement is
         hereby amended and modified to provide that, if on March 29, 2000, the
         sum of the outstanding aggregate principal amount of the Loans and the
         LC Exposure exceeds the lesser of the then effective Borrowing Base or
         the aggregate amount of the Commitments, then the Company shall
         immediately pay or prepay the amount of such excess amount for
         application first, towards the reduction of all amounts previously
         drawn under Letters of Credit, but not yet funded as a Revolving
         Credit Loan pursuant to Section 4.07(b) or reimbursed, second, if
         necessary, towards reduction of the outstanding principal balance of
         the Notes by prepaying Base Rate Loans, if any, then outstanding, and
         third, if necessary, at the election of the Company, either toward a
         reduction of the outstanding principal balance of the Notes by
         prepaying Fixed Rate Loans, if any, then outstanding or by paying such
         amount to the Agent as cash collateral for outstanding Letters of
         Credit, which amount shall be held by the Agent as cash collateral to

                                      -3-

<PAGE>   4
         secure the Company's obligation to reimburse the Agent and the Lenders
         for drawing under the Letters of Credit.

                  2.4  MarketSpan Credit Facility.  Section 8.07 of the Credit
         Agreement is hereby amended in its entirety to read as follows:

                           "Section 8.07 MarketSpan Credit Facility. The
                  Company shall maintain an unused and available commitment
                  under the MarketSpan Credit Facility equal to or greater than
                  the amount by which the Borrowing Base exceeds the Threshold
                  Amount until (i) such time as the Borrowing Base is equal to
                  the Threshold Amount, (ii) such time as any and all
                  prepayments required under Section 2.08(b) have been made in
                  full, and (iii) such time as no Default exists hereunder."

         Section 3.  Borrowing Base; Threshold Amount.  Notwithstanding anything
         to the contrary contained in the Credit Agreement including, without
         limitation, the provisions of Section 2.09:

                  (a) The amount of the Borrowing Base shall be (i)
         $240,000,000 for the period from and including the Effective Date of
         this Third Amendment to but not including March 29, 2000, and (ii) an
         amount equal to the Threshold Amount in effect on March 29, 2000, for
         the period from and including March 29, 2000 to and including
         September 1, 2000, at which time and from time to time thereafter the
         Borrowing Base shall be redetermined in accordance with Section 2.09
         of the Credit Agreement.

                  (b) Any unscheduled redetermination of the Borrowing Base or
         the Threshold Amount which occurs on or before March 29, 2000, must be
         approved by all of the Lenders.

         Section 4. Conditions. In addition to any and all other applicable
conditions precedent contained in Article VI of the Credit Agreement, this
Third Amendment shall become binding upon receipt by the Agent of the following
documents, each of which shall be satisfactory to the Agent in form and
substance:

                  (a)  Counterparts of this Third Amendment duly executed by
         the Company.

                  (b)  Photocopies of all duly completed and executed
         documentation evidencing the extension of the final maturity of the
         MarketSpan Credit Facility from January 1, 2000 to March 31, 2000.

                  (c)  Such other documents as the Agent or its counsel may
         reasonably request.

         Section 5. Extent of Amendments. The parties hereto hereby acknowledge
and agree that, except as specifically supplemented and amended, changed or
modified hereby, the Credit Agreement shall remain in full force and effect in
accordance with its terms.

                                      -4-

<PAGE>   5
         Section 6. Reaffirmation. The Company hereby reaffirms that as of the
date of this Third Amendment, the representations and warranties made by the
Company in Article VII of the Credit Agreement are true and correct on the date
hereof as though made on and as of the date of this Third Amendment.

         Section 7.  Governing Law.  This Third Amendment shall be governed by,
and construed in accordance with, the laws of the State of Texas.

         Section 8. Counterparts. This Third Amendment may be executed in two
or more counter parts, and it shall not be necessary that the signatures of all
parties hereto be contained on any one counterpart hereof; each counterpart
shall be deemed an original, but all of which together shall constitute one and
the same instrument.

         Section 9. Final Agreement. THE CREDIT AGREEMENT, AS AMENDED HEREBY,
THIS THIRD AMENDMENT, THE NOTES AND THE SECURITY INSTRUMENTS REPRESENT THE
FINAL AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF
PRIOR, CONTEMPORANEOUS OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE
NO UNWRITTEN OR ORAL AGREEMENTS BETWEEN THE PARTIES.



                      [SIGNATURE PAGES BEGIN ON NEXT PAGE]


                                      -5-

<PAGE>   6
         IN WITNESS WHEREOF, the parties hereto have caused this Third
Amendment to be duly executed effective as of the date first above written.


                                       COMPANY:

                                       THE HOUSTON EXPLORATION COMPANY


                                       By:   /s/ Thomas W. Powers
                                          --------------------------------
                                       Name:     Thomas W. Powers
                                       Title:    Senior Vice President
                                                 Business Development
                                                 Finance and Treasurer

                                       Address:   1100 Louisiana
                                                  Suite 2000
                                                  Houston, Texas  77002

                                       Telecopier No.:  713/830-6885

                                       Telephone No.:  713/830-6853


                        [Third Amendment to Amended and
                           Restated Credit Agreement
                               Signature Page 1]

<PAGE>   7
                                          LENDERS AND AGENTS:
                                          ------------------

                                          CHASE BANK OF TEXAS, NATIONAL
                                          ASSOCIATION, individually as a
                                            Lender and as Administrative Agent


                                          By: /s/ Russell Johnson
                                             -------------------------------
                                          Name:   Russell Johnson
                                          Title:  Vice President

                                          Applicable Lending Office for Base
                                            Rate Loans:

                                          Address:  712 Main Street
                                                    Houston, Texas  77002

                                          Applicable Lending Office for Fixed
                                            Rate Loans:

                                          Address:    712 Main Street
                                                      Houston, Texas  77002
                                          Telecopier: 713/216-8870
                                          Telephone:  713/216-5617

                                          Address for Notices:

                                          Loan and Agency Services
                                          The Chase Manhattan Bank
                                          1 Chase Manhattan Plaza, 8th Floor
                                          New York, New York  10081

                                          Telecopier No.:  212/552-7490
                                          Telephone No.:   212/552-7943

                                          Attention: Muniram Appanna



                        [Third Amendment to Amended and
                           Restated Credit Agreement
                               Signature Page 2]

<PAGE>   8
                           HE BANK OF NOVA SCOTIA,
                           individually as a Lender and as Syndication
                           Agent

                           By:    /s/F.C.H. Ashby
                              ----------------------------------
                           Name:  F.C.H. Ashby
                           Title: Senior Manager Loan Operations

                           Applicable Lending Office for Base Rate Loans:

                           Address:  600 Peachtree Street N.E.
                                     Suite 2700
                                     Atlanta GA 30308

                           Applicable Lending Office for Fixed Rate Loans:

                           Address:  600 Peachtree Street N.E.
                                     Suite 2700
                                     Atlanta GA 30308

                           Address for Notices:

                                     1100 Louisiana, Suite 3000
                                     Houston, Texas 77002

                                     Telecopier No.:  713/752-2425
                                     Telephone No.:  713/759-3441

                                     Attention: Mark Ammerman

                                     with a copy to:

                                     Address:  600 Peachtree Street N.E.
                                                      Suite 2700
                                                      Atlanta GA 30308
                                    Telecopier:       404/888-8998
                                    Telephone:        404/877-1552
                                    Attention:        Phyllis Walker


                        [Third Amendment to Amended and
                           Restated Credit Agreement
                               Signature Page 3]

<PAGE>   9
                                  FIRST UNION NATIONAL BANK,
                                  Individually as a Lender and as
                                  Documentation Agent

                                  By: /s/ Robert R. Wetteroff
                                     ----------------------------------
                                  Name: Robert R. Wetteroff
                                  Title: Senior Vice President

                                  Applicable Lending Office for Base Rate Loans:

                                  Address:   301 South College Street
                                             Charlotte, North Carolina 28288

                                  Applicable Lending Office for Fixed Rate
                                             Loans:

                                  Address:   301 South College Street
                                             Charlotte, North Carolina 28288

                                  Address for Notices:

                                  1001 Fannin Street
                                  Houston, Texas 77002

                                  Telecopier:    713/650-6354
                                  Telephone No.  713/346-2727

                                  Attention:  Jay Chernosky

                                  with a copy to:

                                  1001 Fannin Street
                                  Houston, Texas 77002

                                  Telecopier:    713/650-6354
                                  Telephone No.  713/346-2727

                                  Attention:  Debbie Blank


                        [Third Amendment to Amended and
                           Restated Credit Agreement
                               Signature Page 4]

<PAGE>   10
                                 PNC BANK NATIONAL ASSOCIATION,
                                 Individually as a Lender and as Managing
                                 Agent

                                 By: /s/ Thomas A. Maleski
                                    --------------------------------
                                 Name: Thomas a. Maleski
                                 Title: Vice President

                                 Applicable Lending Office for Base Rate Loans:

                                 Address:  249 Fifth Avenue, 3rd Floor
                                           Mail Stop P1-POPP-03-1
                                           Pittsburgh, Pennsylvania 15222


                                 Applicable Lending Office for Fixed Rate
                                            Loans:

                                 Address:  249 Fifth Avenue, 3rd Floor
                                           Mail Stop P1-POPP-03-1
                                           Pittsburgh, Pennsylvania 15222

                                 Address for Notices:

                                 249 Fifth Avenue, 3rd Floor
                                 Mail Stop P1-POPP-03-1
                                 Pittsburgh, Pennsylvania 15222

                                 Telecopier:   412/762-2571
                                 Telephone No. 412/762-3025

                                 Attention:  Thomas A. Majeski

                                 with a copy to:

                                 620 Liberty Avenue
                                 Mail Stop P2-PTPP-03-1
                                 Pittsburgh, Pennsylvania 15222

                                 Telecopier:   412/762-5271
                                 Telephone No. 412/762-3025

                                 Attention:  Stephanie Angelini

                        [Third Amendment to Amended and
                           Restated Credit Agreement
                               Signature Page 5]

<PAGE>   11
                                 COMERICA BANK - TEXAS

                                 By: /s/ Martin W. Wilson
                                    ---------------------------------
                                 Name: Martin W. Wilson
                                 Title: Vice President

                                 Applicable Lending Office for Base Rate Loans:

                                 Address:  1601 Elm Street, 2nd Floor
                                           Dallas, Texas 75201


                                 Applicable Lending Office for Fixed Rate
                                            Loans:

                                 Address:  1601 Elm Street, 2nd Floor
                                           Dallas, Texas 75201

                                 Address for Notices:

                                 1601 Elm Street, 2nd Floor
                                 Dallas, Texas 75201

                                 Telecopier:     214/969-6561
                                 Telephone No.   214/969-6563

                                 Attention:  Martin W. Wilson

                                 with a copy to:

                                 Livonia Operations Center
                                 39200 Six Mile Road, 4th Floor
                                 Livonia, Michigan 48152

                                 Telecopier:     734/632-7050
                                 Telephone No.   734/632-3063

                                 Attention:  Nancy Lee

                        [Third Amendment to Amended and
                           Restated Credit Agreement
                               Signature Page 6]

<PAGE>   12
                                       THE BANK OF NEW YORK

                                       By: /s/ Peter Keller
                                          --------------------------
                                       Name: Peter Keller
                                       Title: Vice President

                                       Applicable Lending Office for Base Rate
                                         Loans:

                                       Address:  One Wall Street
                                                 Energy Division, 19th Floor
                                                 New York, New York 10286

                                       Telecopier No.:212/635-7924
                                       Telephone No.: 212/635-7550

                                       Attention:  Kathy D'Elena


                                       Applicable Lending Office for Fixed
                                         Rate Loans:

                                       Address:  One Wall Street
                                                 Energy Division, 19th Floor
                                                 New York, New York 10286

                                       Telecopier No.:212/635-7924
                                       Telephone No.: 212/635-7550

                                       Attention:  Kathy D'Elena

                                       Address for Notices:
                                       The Bank of New York
                                       One Wall Street
                                       Energy Division, 19th Floor
                                       New York, NY  10286

                                       Telecopier No.: 212/635-7924
                                       Telephone No.:  212/635-7550

                                       Attention: Kathy D'Elena


                        [Third Amendment to Amended and
                           Restated Credit Agreement
                               Signature Page 7]

<PAGE>   13
                                            with a copy to:

                                                     Address:
                                            The Bank of New York
                                              One Wall Street
                                            Energy Division, 19th Floor
                                            New York, NY  10286

                                            Telecopier No.: 212/635-7924
                                            Telephone No.:  212/635-7861

                                            Attention: Peter Keller


                        [Third Amendment to Amended and
                           Restated Credit Agreement
                               Signature Page 8]

<PAGE>   14
                                        NATEXIS BANQUE

                                        By: /s/ N. Eric Ditges
                                           -----------------------------
                                        Name: N. Eric Ditges
                                        Title: Vice President

                                        By: /s/ Louis P. Laville, III
                                           -----------------------------
                                        Name: Louis P. Laville, III
                                        Title: Vice President and Group Manager

                                        Applicable Lending Office for Base
                                          Rate Loans:

                                        Address:  645 5th Avenue, 20th Floor
                                                  New York, New York
                                        Telecopier No.:212/872-5045

                                        Applicable Lending Office for Fixed
                                          Rate Loans:

                                        Address:  645 5th Avenue, 20th Floor
                                                  New York, New York
                                        Telecopier No.:212/872-5045

                                        Address for Notices:

                                        Natexis Banque, Southwest
                                            Representative Office
                                        333 Clay Street, Suite 4340
                                        Houston, Texas  77002
                                        Telecopier No.: 713/759-9908
                                        Telephone No.: 713/759-9401

                                        Attention:  Tanya McAllister

                                        with a copy to:

                                        Address:

                                        Natexis Banque, New York Branch
                                        645 5th Avenue, 20th Floor
                                        New York, New York
                                        Telecopier No.: 212/872-5045

                                        Attention: Joan Rankine


                        [Third Amendment to Amended and
                           Restated Credit Agreement
                               Signature Page 9]

<PAGE>   15



                                            Natexis Banque, Southwest
                                                Representative Office
                                            333 Clay Street, Suite 4340
                                            Houston, Texas  77002

                                            Telecopier No.: 713/759-9908
                                            Telephone No.: 713/759-9401

                                            Attention: Eric Ditges



                        [Third Amendment to Amended and
                           Restated Credit Agreement
                               Signature Page 10]

<PAGE>   16
                                       BANK ONE, TEXAS, N.A.


                                       By: /s/ Christine M. Macan
                                       -----------------------------------------
                                       Name: Christine M. Macan
                                       Title: Vice President

                                       Applicable Lending Office for Base
                                         Rate Loans:

                                       Address:   910 Travis, TX2-4330
                                                  Houston, Texas 77002

                                       Applicable Lending Office for Fixed
                                         Rate Loans:

                                       Address:   910 Travis, TX2-4330
                                                  Houston, Texas 77002

                                       Address for Notices:

                                       Bank One Center
                                       910 Travis, TX2-4330
                                       Houston, Texas 77002

                                       Telecopier No.: 713/751-3544
                                       Telephone No.: 713/751-3484

                                       Attention: Christine Macan

                                       with a copy to:

                                       Address:   Bank One Center
                                                  910 Travis, TX2-4375
                                                  Houston, Texas 77002

                                       Telecopier No.: 713/751-3982
                                       Telephone No.:  713/751-6174

                                       Attention:  Jeanie Harman

                                      and


                        [Third Amendment to Amended and
                           Restated Credit Agreement
                               Signature Page 11]

<PAGE>   17
                                      Address:   500 Throckmorton
                                                 West Complex PG6
                                                 Fort Worth, Texas 76102

                                      Telecopier No.: 817/884-4651
                                      Telephone No.:  817/884-4399

                                      Attention:  Carol Peacock




                        [Third Amendment to Amended and
                           Restated Credit Agreement
                               Signature Page 12]

<PAGE>   18
                                       HIBERNIA NATIONAL BANK

                                       By: /s/ David R. Reid
                                       -----------------------------------------
                                       Name: David R. Reid
                                       Title: Senior Vice President

                                       Applicable Lending Office for Base
                                         Rate Loans:

                                       Address:   313 Carondelet Street
                                                  New Orleans, Louisiana 70130

                                       Applicable Lending Office for Fixed
                                         Rate Loans:

                                       Address:   313 Carondelet Street
                                                  New Orleans, Louisiana 70130

                                       Address for Notices:

                                       213 W. Vermilion
                                       Lafayette, Louisiana 70501

                                       Telecopier No.: 318/268-4566
                                       Telephone No.:  318/268-4582

                                       Attention: David Reid

                                       with a copy to:

                                       Address:   313 Carondelet Street
                                                  New Orleans, Louisiana 70130

                                       Telecopier No.: 504/533-5434
                                       Telephone No.:  504/533-5717

                                       Attention: Spencer Gagnet


                        [Third Amendment to Amended and
                           Restated Credit Agreement
                               Signature Page 13]

                                      and

<PAGE>   19
                                        Address:  313 Carondelet Street
                                                  New Orleans, Louisiana 70130

                                        Telecopier No.: 504/533-5434
                                        Telephone No.:  504/533-5352

                                        Attention: Virginia Bell Cowart