<PAGE>
 
                                          Exhibit (10)-23
                                          Unicom Corporation and
                                          Commonwealth Edison Company
                                          Form 10-K File Nos. 1-11375 and 1-1839


                              UNICOM CORPORATION
                             STOCK AWARD AGREEMENT
                                        

Unicom Corporation, an Illinois corporation (the "Company"), hereby grants
Oliver D. Kingsley, Jr., (the "Holder") as of January 25, 1999, (the "Grant
Date"), pursuant to the provisions of the Unicom Corporation Long-Term Incentive
Plan (the "Plan"), a stock award (the "Award") of 6,500 shares of the Company's
Common Stock, without par value ("Common Stock"), upon and subject to the terms
and conditions set forth below.  Capitalized terms not defined herein shall have
the meanings specified in the Plan.

1.   Award Subject to Acceptance of Agreement.
     ---------------------------------------- 

The Award shall be subject to all the terms of this Agreement and the Plan.

2.   Rights as a Stockholder; Dividend Equivalents.
     --------------------------------------------- 

The Holder shall not be entitled to any privileges of ownership with respect to
the shares of Common Stock subject to the Award unless and until, and only to
the extent, such shares become vested pursuant to Section 3 hereof and the
Holder becomes a stockholder of record with respect to such shares.  The Company
shall pay to the Holder a cash payment equal to the amount of any dividends he
would have received had the shares of Common Stock covered by this Award been
issued to him on the date hereof and such payment shall be made when and as
dividends are paid on outstanding shares of Common Stock until such shares
either vest or are forfeited, as provided in Section 3.

3.   Vesting.
     ------- 

     (a)  The Award shall vest with respect to 6,500 shares of Common Stock on
          January 25, 2000, or earlier pursuant to Sections 3(b) and 3(c) hereof
          (such period hereinafter referred to as the "Vesting Period").

     (b)  If (i) the Holder's employment by the Company or its successors
          terminates by reason of the Holder's retirement, Disability or death,
          the Award shall become fully vested as of the date of such retirement,
          Disability or death.

     (c)  If (i) the Holder's employment is terminated by the Company or its
          successors for any reason other than a reason described in Section
          3(d), the Award shall become fully vested as of the effective date of
          such termination of employment, as applicable.

     (d)  If the Holder's employment is terminated by the Company for Cause, the
          portion of the Award that is not vested as of the effective date of
          such termination of employment shall be forfeited by the Holder, and
          such portion shall be canceled by the Company.

4.   Termination of Award.
     -------------------- 

In the event that the Holder shall forfeit all or a portion of the shares of
Common Stock subject to the Award, this Award shall terminate.  The Holder
shall, upon the Company's request, promptly return this Agreement to the Company
for cancellation.  Such cancellation shall be effective regardless of whether
the Holder returns this Agreement.
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Stock Award Agreement-Oliver D. Kingsley, Jr.
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5.   Additional Terms and Conditions of Award.
     ---------------------------------------- 

     5.1. Nontransferability of Award.
          --------------------------- 

     During the Vesting Period, this Award may not be sold, transferred,
     assigned, pledged, hypothecated, encumbered or otherwise disposed of
     (whether by operation of law or otherwise) or be subject to execution,
     attachment or similar process, other than by will or the laws of descent
     and distribution.  Upon any attempt to so sell, transfer, assign, pledge,
     hypothecate or encumber, or otherwise dispose of this Award or any shares
     subject hereto that have not been issued pursuant to Section 5.5 shall
     immediately become null and void.

     5.2. Withholding Taxes.
          ----------------- 

          (a)  As a condition precedent to the delivery to the Holder of any
          shares of Common Stock subject to the Award, the Holder shall, upon
          request by the Company, pay to the Company (or shall cause a broker-
          dealer on behalf of the Holder to pay to the Company) such amount of
          cash as the Company may be required, under all applicable federal,
          state, local or other laws or regulations, to withhold and pay over as
          income or other withholding taxes (the "Required Tax Payments") with
          respect to the Award.  If the Holder shall fail to advance the
          Required Tax Payments after request by the Company, the Company may,
          in its discretion, deduct any Required Tax Payments from any amount
          then or thereafter payable by the Company to the Holder.

          (b)  The Holder may elect to satisfy his or her obligation to advance
          the Required Tax Payments by any of the following means:  (1) a cash
          payment to the Company pursuant to Section 5.2(a), (2) delivery to the
          Company of previously owned whole shares of Common Stock (which the
          Holder has held for at least six months prior to the delivery of such
          shares or which the Holder purchased on the open market and for which
          the Holder has good title, free and clear of all liens and
          encumbrances) having a Fair Market Value, determined as of the date
          the obligation to withhold or pay taxes first arises in connection
          with the Award (the "Tax Date"), equal to the Required Tax Payments,
          (3) authorizing the Company to withhold from the shares of Common
          Stock otherwise to be delivered to the Holder pursuant to the Award, a
          number of whole shares of Common Stock having a Fair Market Value,
          determined as of the Tax Date, equal to the Required Tax Payments, (4)
          a cash payment by a broker-dealer acceptable to the Company through
          whom the Holder has sold the shares with respect to which the Required
          Tax Payments have arisen or (5) any combination of (1), (2) and (3).
          The Committee shall have sole discretion to disapprove of an election
          pursuant to any of clauses (2)-(5).  Shares of Common Stock to be
          delivered or withheld may have a Fair Market Value in excess of the
          minimum amount of the Required Tax Payments, but not in excess of the
          amount determined by applying the Holder's maximum marginal tax rate.
          Any fraction of a share of Common Stock which would be required to
          satisfy such an obligation shall be disregarded and the remaining
          amount due shall be paid in cash by the Holder.  No certificate
          representing a share of Common Stock shall be delivered until the
          Required Tax Payments have been satisfied in full.

     5.3. Adjustment.
          ---------- 

     In the event of any stock split, stock dividend, recapitalization,
     reorganization, merger, consolidation, combination, exchange of shares,
     liquidation, spin-off or other similar change in capitalization or event,
     or any distribution to holders of Common Stock other than a regular cash
     dividend, the number and class of securities subject to the Award shall be
     appropriately adjusted by the Committee.  If any adjustment would result in
     a fractional security being subject to the Award, the Company shall pay the
     Holder, in connection with the vesting, if any, of such 
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Stock Award Agreement-Oliver D. Kingsley, Jr.
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     fractional security, an amount in cash determined by multiplying (i) such
     fraction (rounded to the nearest hundredth) by (ii) the Fair Market Value
     on the vesting date. The decision of the Committee regarding any such
     adjustment shall be final, binding and conclusive.

     5.4. Compliance with Applicable Law.
          ------------------------------ 

     The Award is subject to the condition that if the listing, registration or
     qualification of the shares subject to the Award upon any securities
     exchange or under any law, or the consent or approval of any governmental
     body, or the taking of any other action is necessary or desirable as a
     condition of, or in connection with, the vesting or delivery of shares
     hereunder, the shares of Common Stock subject to the Award shall not vest
     or be delivered, in whole or in part, unless such listing, registration,
     qualification, consent or approval shall have been effected or obtained,
     free of any conditions not acceptable to the Company.  The Company agrees
     to use reasonable efforts to effect or obtain any such listing,
     registration, qualification, consent or approval.

     5.5. Delivery of Certificates.
          ------------------------ 

     Subject to Section 5.2, as soon as practicable after the vesting of the
     Award, in whole or in part, the Company shall deliver or cause to be
     delivered one or more certificates issued in the Holder's name representing
     the number of vested shares.  The Company shall pay all original issue or
     transfer taxes and all fees and expenses incident to such delivery, except
     as otherwise provided in Section 5.2.

     5.6. Award Confers No Rights to Continued Employment.
          ----------------------------------------------- 

     In no event shall the granting of the Award or its acceptance by the Holder
     give or be deemed to give the Holder any right to continued employment by
     the Company or any affiliate of the Company.

     5.7. Decisions of Committee.
          ---------------------- 

     The Committee shall have the right to resolve all questions which may arise
     in connection with the Award.  Any interpretation, determination or other
     action made or taken by the Committee regarding the Plan or this Agreement
     shall be final, binding and conclusive.

     5.8. Company to Reserve Shares.
          ------------------------- 

     The Company shall at all times prior to the cancellation of the Award
     reserve and keep available, either in its treasury or out of its authorized
     but unissued shares of Common Stock, the full number of unvested shares
     subject to the Award from time to time.

     5.9. Agreement Subject to the Plan.
          ----------------------------- 

     This Agreement is subject to the provisions of the Plan and shall be
     interpreted in accordance therewith.  The Holder hereby acknowledges
     receipt of a copy of the Plan.

6.   Miscellaneous Provisions.
     ------------------------ 

     6.1. Meaning of Certain Terms.
          ------------------------ 

     As used herein, the following terms shall have the respective meanings set
     forth below:

     "Cause" shall mean:

          (1) the Holder's willful commission of acts or omissions which have,
     have had, or are 
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Stock Award Agreement-Oliver D. Kingsley, Jr.
Page 4

     likely to have a material adverse effect on the business,
     operations, financial condition or reputation of the Company or any of its
     affiliates;

          (2) the Holder's conviction (including a plea of guilty or nolo
     contendere) of a felony or any crime of fraud, theft, dishonesty or moral
     turpitude; or,

          (3) the Holder's material violation of any statutory or common law
     duty of loyalty to the Company or any of its affiliates.

     "Disability" shall have the meaning specified in any long-term disability
     plan or arrangement maintained by the Company or an affiliate under which
     the Holder is covered or, if no such plan or arrangement is then in effect,
     as determined by the Committee.

     "Fair Market Value" means the closing transaction price of a share of
     Common Stock, as reported on the New York Stock Exchange Composite
     Transactions on the date in question or, if there shall be no reported
     transaction for such date, on the next preceding date for which a
     transaction was reported.

     "vest" means no longer subject to forfeiture.

     As used herein, employment by the Company shall include employment by a
     corporation which is a "subsidiary corporation" of the Company, as such
     term is defined in section 424 of the Code.  References in this Agreement
     to sections of the Code shall be deemed to refer to any successor section
     of the Code or any successor internal revenue law.

     6.2. Successors.
          ---------- 

     This Agreement shall be binding upon and inure to the benefit of any
     successor or successors of the Company and any person or persons who shall,
     upon the death of the Holder, acquire any rights hereunder in accordance
     with this Agreement or the Plan.

     6.3. Notices.
          ------- 

     All notices, requests or other communications provided for in this
     Agreement shall be made, if to the Company, to Unicom Corporation, 10 South
     Dearborn Street -- 37th Floor, Chicago, Illinois 60603, Attention:
     Secretary, and if to the Holder, ____________________________.  All
     notices, requests or other communications provided for in this Agreement
     shall be made in writing (a) by personal delivery to the party entitled
     thereto, (b) by facsimile transmission with confirmation of receipt, (c) by
     mailing in the United States mails to the last known address of the party
     entitled thereto or (d) by express courier service.  The notice, request or
     other communication shall be deemed to be received upon personal delivery,
     upon confirmation of receipt of facsimile transmission, or upon receipt by
     the party entitled thereto if by United States mail or express courier
     service; provided, however, that if a notice, request or other
     communication is not received during regular business hours, it shall be
     deemed to be received on the next succeeding business day of the Company.

     6.4. Governing Law.
          ------------- 

     This Agreement, the Award and all determinations made and actions taken
     pursuant hereto and thereto, to the extent not otherwise governed by the
     laws of the United States, shall be governed by the laws of the State of
     Illinois and construed in accordance therewith without giving effect to
     conflicts of laws principles.
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Stock Award Agreement-Oliver D. Kingsley, Jr.
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     6.5. Counterparts.
          ------------ 
     
     This Agreement may be executed in two or more counterparts each of which
     shall be deemed an original and both of which together shall constitute one
     and the same instrument.


                                    UNICOM CORPORATION


                                    By:______________________________
                                       John P. McGarrity
                                       Secretary