<PAGE>   1
                                                                      EXHIBIT 25




                     SECURITIES AND EXCHANGE COMMISSION
                          WASHINGTON,  D. C.  20549

                          ------------------------

                                  FORM  T-1

                          STATEMENT OF ELIGIBILITY
                  UNDER THE TRUST INDENTURE ACT OF 1939 OF
                 A CORPORATION DESIGNATED TO ACT AS TRUSTEE

                          ------------------------

                    CHECK IF AN APPLICATION TO DETERMINE
                    ELIGIBILITY OF A TRUSTEE PURSUANT TO
                           SECTION 305(b)(2) ____

                          ------------------------

                   UNITED STATES TRUST COMPANY OF NEW YORK
             (Exact name of trustee as specified in its charter)

           New York                                        13-3818954
(Jurisdiction of incorporation                         (I. R. S. Employer
if not a U. S. national bank)                          Identification No.)

    114 West 47th Street                                      10036
      New York, New York                                   (Zip Code)
    (Address of principal
      executive offices)                                       

                         --------------------------
                        Chesapeake Energy Corporation
             (Exact name of OBLIGOR as specified in its charter)

                Oklahoma                                        73-1395733
    (State or other jurisdiction of                         (I. R. S. Employer
     incorporation or organization)                         Identification No.)

       6100 North Western Avenue                                   73118
        Oklahoma City, Oklahoma                                 (Zip code)
(Address of principal executive offices)

                         --------------------------
                             The Ames Company, Inc.
             (Exact name of REGISTRANT as specified in its charter)

            Oklahoma                                        73-1470082
(State or other jurisdiction of                         (I. R. S. Employer
 incorporation or organization)                         Identification No.)

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                                     - 2 -

                             ADDITIONAL REGISTRANTS

                       Chesapeake Acquisition Corporation
             (Exact name of REGISTRANT as specified in its charter)

            Oklahoma                                        73-1528271
(State or other jurisdiction of                         (I. R. S. Employer
 incorporation or organization)                         Identification No.)

                         --------------------------
                         Chesapeake Canada Corporation
             (Exact name of REGISTRANT as specified in its charter)

        Alberta, Canada                                   Not Applicable
(State or other jurisdiction of                         (I. R. S. Employer
 incorporation or organization)                         Identification No.)

                         --------------------------
                    Chesapeake Energy Louisiana Corporation
             (Exact name of REGISTRANT as specified in its charter)

            Oklahoma                                        73-1524569
(State or other jurisdiction of                         (I. R. S. Employer
 incorporation or organization)                         Identification No.)

                         --------------------------
                            Chesapeake Gothic Corp.
             (Exact name of REGISTRANT as specified in its charter)

            Oklahoma                                        73-1532892
(State or other jurisdiction of                         (I. R. S. Employer
 incorporation or organization)                         Identification No.)

                         --------------------------
                         Chesapeake Mid-Continent Corp.
             (Exact name of REGISTRANT as specified in its charter)

            Oklahoma                                        73-1529077
(State or other jurisdiction of                         (I. R. S. Employer
 incorporation or organization)                         Identification No.)

                         --------------------------          
                           Chesapeake Operating, Inc.
             (Exact name of REGISTRANT as specified in its charter)

            Oklahoma                                        73-1343196
(State or other jurisdiction of                         (I. R. S. Employer
 incorporation or organization)                         Identification No.)
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                                     - 3 -


                         --------------------------          
                              Sunoma Energy Corp.
             (Exact name of REGISTRANT as specified in its charter)

        Alberta, Canada                                   Not Applicable
(State or other jurisdiction of                         (I. R. S. Employer
 incorporation or organization)                         Identification No.)

                         --------------------------          
                   Chesapeake Exploration Limited Partnership
             (Exact name of REGISTRANT as specified in its charter)

            Oklahoma                                        73-1384282
(State or other jurisdiction of                         (I. R. S. Employer
 incorporation or organization)                         Identification No.)

                         --------------------------          
                           Chesapeake Louisiana, L.P.
             (Exact name of REGISTRANT as specified in its charter)

            Oklahoma                                        73-1519126
(State or other jurisdiction of                         (I. R. S. Employer
 incorporation or organization)                         Identification No.)

                         --------------------------          
                    Chesapeake Panhandle Limited Partnership
             (Exact name of REGISTRANT as specified in its charter)

            Delaware                                        95-4601927
(State or other jurisdiction of                         (I. R. S. Employer
 incorporation or organization)                         Identification No.)

                         --------------------------          
                     9 5/8% Series B Senior Notes due 2005
                      (Title of the indenture securities)


================================================================================

<PAGE>   4
                                     - 4 -


                                    GENERAL


 1.      General Information

         Furnish the following information as to the trustee:

         (a)     Name and address of each examining or supervising authority to
                 which it is subject.

                 Federal Reserve Bank of New York (2nd District), New York, New
                          York (Board of Governors of the Federal Reserve
                          System).
                 Federal Deposit Insurance Corporation,  Washington,  D. C.
                 New York State Banking Department, Albany, New York

         (b)     Whether it is authorized to exercise corporate trust powers.

                          The trustee is authorized to exercise corporate trust
                          powers.


 2.      Affiliations with the Obligor

         If the obligor is an affiliate of the trustee, describe each such
         affiliation.

         None.

3,4,5,6,7,8,9,10,11,12,13,14 and 15.

         Chesapeake Energy Corporation is currently not in default under any of
         its outstanding securities for which United States Trust Company of
         New York is Trustee.  Accordingly, responses to Items 3, 4, 5, 6, 7,
         8, 9, 10, 11, 12, 13, 14 and 15 of Form T-1 are not required under
         General Instruction B.

16.      List of Exhibits

         T-1.1   --       Organization Certificate, as amended, issued by the
                          State of New York Banking Department to transact
                          business as a Trust Company, is incorporated by
                          reference to Exhibit T-1.1 to Form T-1 filed on
                          September 15, 1995 with the Commission pursuant to
                          the Trust Indenture Act of 1939, as amended by the
                          Trust Indenture Reform Act of 1990 (Registration No.
                          33-97056).
<PAGE>   5
                                     - 5 -


16.      List of Exhibits
         (cont'd)


        T-1.2    --       Included in Exhibit T-1.1.

        T-1.3    --       Included in Exhibit T-1.1.

        T-1.4    --       The By-Laws of United States Trust Company of New
                          York, as amended, is incorporated by reference to
                          Exhibit T-1.4 to Form T-1 filed on September 15, 1995
                          with the Commission pursuant to the Trust Indenture
                          Act of 1939, as amended by the Trust Indenture Reform
                          Act of 1990 (Registration No. 33-97056).

        T-1.6    --       The consent of the trustee required by Section 321(b)
                          of the Trust Indenture Act of 1939, as amended by the
                          Trust Indenture Reform Act of 1990.

        T-1.7    --       A copy of the latest report of condition of the
                          trustee pursuant to law or the requirements of its
                          supervising or examining authority.


                                      NOTE


         As of June 17, 1998, the trustee had 2,999,020 shares of Common Stock
         outstanding, all of which are owned by its parent company, U. S. Trust
         Corporation.  The term "trustee" in Item 2, refers to each of United
         States Trust Company of New York and its parent company, U. S. Trust
         Corporation.

         In answering Item 2 in this statement of eligibility, as to matters
         peculiarly within the knowledge of the obligor or its directors, the
         trustee has relied upon information furnished to it by the obligor and
         will rely on information to be furnished by the obligor and the
         trustee disclaims responsibility for the accuracy or completeness of
         such information.


                         --------------------------

<PAGE>   6
                                     - 6 -



         Pursuant to the requirements of the Trust Indenture Act of 1939, the
         trustee, United States Trust Company of New York, a corporation
         organized and existing under the laws of the State of New York, has
         duly caused this statement of eligibility to be signed on its behalf
         by the undersigned, thereunto duly authorized, all in the City of New
         York, and State of New York, on the 17th day of June, 1998.


         UNITED STATES TRUST COMPANY OF
                 NEW YORK, Trustee


By:      /s/ GERARD F. GANEY
         ---------------------------------
         Gerard F. Ganey
         Senior Vice President




<PAGE>   7


                                                                   EXHIBIT T-1.6

      The consent of the trustee required by Section 321(b) of the Act.

                   United States Trust Company of New York
                          114 West 47th Street New
                               York, NY  10036


September 1, 1995



Securities and Exchange Commission
450 5th Street, N.W.
Washington, DC  20549

Gentlemen:

Pursuant to the provisions of Section 321(b) of the Trust Indenture Act of
1939, as amended by the Trust Indenture Reform Act of 1990, and subject to the
limitations set forth therein, United States Trust Company of New York ("U.S.
Trust") hereby consents that reports of examinations of U.S. Trust by Federal,
State, Territorial or District authorities may be furnished by such authorities
to the Securities and Exchange Commission upon request therefor.




Very truly yours,


UNITED STATES TRUST COMPANY
         OF NEW YORK


         
                                                   
By:      /s/ GERARD F. GANEY
         ------------------------------------------
         Gerard F. Ganey
         Senior Vice President
<PAGE>   8
                                                                   EXHIBIT T-1.7

                    UNITED STATES TRUST COMPANY OF NEW YORK
                      CONSOLIDATED STATEMENT OF CONDITION
                                 MARCH 31, 1998
                                ($ IN THOUSANDS)

<TABLE>
<S>                                                                                <C>
ASSETS
------
Cash and Due from Banks                                                            $      303,692

Short-Term Investments                                                                    325,044

Securities, Available for Sale                                                            650,954

Loans                                                                                   1,717,101
Less:  Allowance for Credit Losses                                                         16,546
                                                                                     ------------
     Net Loans                                                                          1,700,555
Premises and Equipment                                                                     58,868
Other Assets                                                                              120,865
                                                                                      -----------
     TOTAL ASSETS                                                                      $3,159,978
                                                                                       ==========

LIABILITIES
-----------
Deposits:
     Non-Interest Bearing                                                            $    602,769
     Interest Bearing                                                                   1,955,571
                                                                                       ----------
        Total Deposits                                                                  2,558,340

Short-Term Credit Facilities                                                              293,185
Accounts Payable and Accrued Liabilities                                                  136,396
                                                                                        ---------
     TOTAL LIABILITIES                                                                 $2,987,921
                                                                                       ==========

STOCKHOLDER'S EQUITY
--------------------
Common Stock  14,995
Capital Surplus                                                                            49,541
Retained Earnings                                                                         105,214
Unrealized Gains on Securities
     Available for Sale (Net of Taxes)                                                      2,307
                                                                                   --------------

TOTAL STOCKHOLDER'S EQUITY                                                                172,057
                                                                                      -----------
    TOTAL LIABILITIES AND
     STOCKHOLDER'S EQUITY                                                              $3,159,978
                                                                                       ==========
</TABLE>

I, Richard E. Brinkmann, Senior Vice President & Comptroller of the named bank
do hereby declare that this Statement of Condition has been prepared in
conformance with the instructions issued by the appropriate regulatory
authority and is true to the best of my knowledge and belief.

Richard E. Brinkmann, SVP & Controller

May 6, 1998