<PAGE>   1

                                                                    Exhibit 10.1

        
                                    AGREEMENT

         This Agreement, made and executed as of May 21, 1997, is between
Albertson's, Inc. and the J.A. and Kathryn Albertson Foundation, Inc. Except
where defined in context, capitalized terms used herein are defined in Article
One.

                              W I T N E S S E T H:

         WHEREAS, the Foundation desires to acquire 20,842,446 shares of Common
Stock (the "Transfer Shares") Beneficially Owned by Alscott Limited Partnership
#1, a Texas limited partnership (the "Partnership"); and

         WHEREAS, the Company is willing to waive whatever rights it may have
under certain existing agreements among the Company, members of the Albertson
family and the Partnership relating to such Transfer Shares and to consent to
the transfer thereof to the Foundation, if the Foundation agrees to be bound by
the terms and conditions of this Agreement.

         NOW, THEREFORE, in consideration of the mutual covenants and agreements
contained herein, the receipt and sufficiency of which are hereby acknowledged,
the parties hereto hereby agree as follows:

                                   ARTICLE ONE

         Section 1.1 Definitions. Except as otherwise specified herein, defined
terms used in this Agreement shall have the following respective meanings:

         "Additional Election Period" shall have the meaning ascribed to it in
         Section 3.1(c).

         "Agreement" shall mean this Agreement.

         "Beneficially Own" shall have the meaning ascribed to it in Rule 13d-3
         under the 1934 Act.

         "Business Day" shall mean any day other than a day on which banks are
         permitted or required to be closed in New York, New York.

         "Closing" shall mean the closing of any purchase of the Offered Shares
         by the Company pursuant to Article 3, which shall be held at 10:00
         A.M., local time, on the Closing Date at the principal office of the
         Company, or at such other time or place as the parties hereto may
         mutually agree.

         "Closing Date" shall have the meaning ascribed to it in Section 3.1(e).

         "Common Stock" shall mean the Common Stock of the Company, par value
         $1.00 per share.

         "Company" shall mean Albertson's, Inc., a Delaware corporation.

         "Company's Notice" shall have the meaning ascribed to it in Section
         3.1(b).



                                        1
<PAGE>   2
         "Control" shall have the meaning ascribed to it in Rule 12b-2 under the
         1934 Act.

         "Donation" shall have the meaning ascribed to it in Section 3.3.

         "Donee's Notice" shall have the meaning ascribed to it in Section 3.3.

         "Election Period" shall mean the five Business Days following giving of
         the Foundation's Notice.

         "Extended Election Period" shall mean the 20 Business Days following
         giving of the Foundation's Notice.

         "Foundation" shall mean the J.A. and Kathryn Albertson Foundation,
         Inc., an Idaho corporation.

         "Foundation's Notice" shall have the meaning ascribed to it in Section
         3.1(a).

         "Group" shall have the meaning ascribed to it in Section 13(d)(3) of
         the 1934 Act.

         "Market Price" shall mean the average of the daily closing prices per
         share of Voting Securities of the same class as the Offered Shares or
         the Voting Securities received in the Donation, as the case may be, for
         the 30 consecutive Trading Days immediately preceding either the day
         that the Foundation's Notice is given pursuant to Section 3.1 or
         Section 3.2 or the day on which Beneficial Ownership is transferred to
         the donee pursuant to Section 3.3, as the case may be.

         "1933 Act" shall mean the Securities Act of 1933, as amended.

         "1934 Act" shall mean the Securities Exchange Act of 1934, as amended.

         "Offered Shares" shall mean the Voting Securities proposed to be
         transferred by the Foundation, the number of which shall be set forth
         in the Foundation's Notice.

         "Person" shall mean any individual, partnership, corporation, group,
         syndicate, trust, government or agency thereof, or any other
         association or entity.

         "Purchase Price" shall mean 96% of the Market Price.

         "Prohibition Notice" shall have the meaning ascribed to it in Section
         3.2(a).

         "Term" shall have the meaning ascribed to it in Section 2.1.

         "Total Voting Power" shall mean the total combined Voting Power of all
         the Voting Securities then outstanding, including, without limitation,
         the Common Stock.

         "Trading Day" shall mean a day on which the principal national
         securities exchange on which the Voting Securities are listed or
         admitted to trading is open for the transaction of business.



                                       2
<PAGE>   3
         "Transfer Shares" shall have the meaning ascribed to it in the recitals
         to this Agreement.

         "Voting Securities" shall mean any securities entitled to vote
         generally in the election of directors of the Company.

         "Voting Power" shall mean voting power in the general election of
         directors of the Company.

         Section 1.2 Calendar Days. Unless otherwise specified, all references
to "days" shall be deemed to be references to calendar days.

                                   ARTICLE TWO

         Section 2.1 Term. The term of this Agreement (the "Term") shall
commence on the date hereof and shall continue until the twentieth anniversary
of the date hereof; provided, however, that the Company may, on three occasions,
by notice given to the Foundation at least 10 days prior to the date on which
this Agreement would otherwise expire, extend the Term for an additional
ten-year period, but in no event shall the Term be extended beyond the fiftieth
anniversary of the date hereof without the written consent of the Foundation;
provided, further, that, not withstanding the foregoing, this Agreement shall
terminate for all purposes, may not be extended and shall be of no further force
or effect on the first day that the Foundation does not Beneficially Own any
Voting Securities.

         Section 2.2 Automatic Termination. Notwithstanding anything to the
contrary set forth herein, this Agreement shall immediately terminate and be of
no further force or effect whatsoever if Beneficial Ownership of the Transfer
Shares is not vested in the Foundation on or before June 30, 1997.

                                  ARTICLE THREE

         Section 3.1 Right of First Refusal.

                  (a) Subject to the provisions of Section 4.1, if the
         Foundation desires to transfer any Voting Securities Beneficially Owned
         by it, the Foundation shall give notice (the "Foundation's Notice") to
         the Company (i) stating that it desires to make such transfer and (ii)
         setting forth the number of Offered Shares. Except as provided in
         Section 3.2(b), the Foundation's Notice shall constitute an irrevocable
         offer by the Foundation to sell the Offered Shares to the Company.

                  (b) Except as otherwise provided in this Article 3, the
         Company may elect to purchase all (but not less than all) of the
         Offered Shares at a price per share equal to the Purchase Price by
         giving notice (the "Company's Notice") to the Foundation during the
         Election Period, stating the Company's irrevocable acceptance of the
         offer set forth in the Foundation's Notice.

                  (c) If the Company does not give the Company's Notice during
         the Election Period, then the Foundation may, for a period of 45 days
         immediately following the expiration of the Election Period, sell the
         Offered Shares at a price per share at or above the Market Price;
         provided, however, that prior to selling (or agreeing to sell) to a
         third party any part of the Offered Shares with aggregate Voting Power,
         on an issued and outstanding basis, in excess of 1% of the Total Voting
         Power, the Foundation shall give the Company notice of the identity of
         such 




                                       3
<PAGE>   4
         third party (and the identity of any known transferee ) and, provided
         that the identity of such third party (and such transferee) has not
         been disclosed to the Company in the Foundation's Notice, the Company
         shall thereupon have three additional Business Days (the "Additional
         Election Period") following giving of such notice during which to elect
         to purchase such part of the Offered Shares at a price per share equal
         to the Purchase Price by giving the Company's Notice.

                  (d) If the Company does not give the Company's Notice during
         the Election Period, any Additional Election Period or the Extended
         Election Period, and the Foundation has not sold all of the Offered
         Shares prior to the expiration of the 45-day period immediately
         following the Election Period or the Extended Election Period, as the
         case may be, the right of first refusal under this Section 3.1 shall
         again apply to any subsequently proposed transfer of any of the Offered
         Shares.

                  (e) Any purchase of any Offered Shares by the Company pursuant
         to this Article 3 shall be completed on a date (the "Closing Date")
         designated by the Company in a notice to the Foundation, which date
         shall be not more than three Business Days following giving of the
         Company's Notice; provided, however, in the event the Company is unable
         to obtain financing sufficient to enable it to effect the purchase of
         the Offered Shares within three Business Days following giving of the
         Company's Notice, the Company may, by giving notice to the Foundation
         during such three-Business Day period, postpone the Closing Date to a
         date not more than 30 days following giving of the Company's Notice;
         provided further that the Company shall pay to the Foundation interest
         on the purchase price of the Offered Shares for each day the Closing
         Date is postponed beyond the expiration of such three-Business Day
         period at a rate of interest per annum equal to the 30-day commercial
         paper high-grade unsecured notes sold through dealers by major
         corporations rate listed in the Wall Street Journal under the heading
         "Money Rates" (or the closest equivalent rate if such rate has ceased
         to be published) on the first Business Day with respect to which such
         interest is payable.

                  (f) The Purchase Price for any Offered Shares purchased by the
         Company pursuant to this Article 3, including any interest provided for
         herein, shall be paid at the Closing by wire transfer of immediately
         available funds to an account previously designated by the Foundation.

                  (g) At the Closing, the Foundation shall deliver to the
         Company certificates representing the shares of Voting Securities being
         sold, free and clear of any lien, claim or encumbrance, together with
         any other documents reasonably necessary to evidence ownership and
         authority to complete the transaction.

         Section 3.2 Certain Limitations. If the Foundation's Notice is given at
a time when the Company is prohibited by any United States securities law, or
any rule or regulation promulgated thereunder, from purchasing the Offered
Shares the following additional provisions shall apply:

                  (a) The Company shall give the Foundation notice of such
         prohibition (the "Prohibition Notice") during the Election Period, and
         the Company may thereafter elect to purchase the Offered Shares by
         giving the Company's Notice at any time during the Extended Election
         Period. If the Company does not give the Company's Notice during the
         Extended Election Period, then the Foundation may, for a period of 45
         days immediately following the 



                                       4
<PAGE>   5
         expiration of the Extended Election Period, sell the Offered Shares at
         a price per share at or above the Market Price; provided, however, that
         prior to selling (or agreeing to sell) to a third party any part of the
         Offered Shares with aggregate Voting Power, on an issued and
         outstanding basis, in excess of 1% of the Total Voting Power, the
         Foundation shall give the Company notice of the identity of such third
         party (and the identity of any known transferee of such third party )
         and, provided that the identity of such third party (and such
         transferee) has not been disclosed to the Company in the Foundation's
         Notice, the Company shall thereupon have the Additional Election Period
         following giving of such notice during which to elect to purchase such
         part of the Offered Shares at a price per share equal to the Purchase
         Price by giving the Company's Notice; or

                  (b) The Company may, if such prohibition arises under any law,
         rule or regulation relating to trading in securities while in the
         possession of material non-public information, disclose such
         information to the Foundation without the Foundation's consent if, but
         only if, the Company has given the Company's Notice during the
         applicable period. In the event the Company discloses information
         pursuant to this Section 3.2(b), the Foundation shall maintain the
         confidentiality of such information, and the Foundation may revoke the
         Foundation's Notice by written notice to the Company given within five
         Business Days following the disclosure of such information by the
         Company to the Foundation. If the Foundation does not elect to revoke
         the Foundation's Notice as provided in the preceding sentence, the
         Company shall be obligated to purchase all (but not less than all) of
         the Offered Shares in accordance with the Company's Notice, and, if
         such purchase is not completed, the Foundation shall have, in addition
         to any other legal or equitable remedy that may be available to it, the
         right of specific performance, as provided in Section 6.1(a) hereof.

         Section 3.3 Charitable Donations. Notwithstanding the limitation on
transfer set forth in Section 3.1, in each calendar year during the Term the
Foundation may make a charitable donation (a "Donation") in the form of Voting
Securities of up to 5% of the total number of Voting Securities Beneficially
Owned by the Foundation at the time of any Donation, provided that the donee has
theretofore agreed (i) to offer to sell to the Company immediately, by written
notice to the Company to be given within three days following receipt of the
Donation (the "Donee's Notice"), all of the Voting Securities received in such
Donation at a price per share equal to the Purchase Price and, if the Company
accepts the offer set forth in the Donee's Notice by written notice to the donee
within five Business Days following giving of the Donee's Notice, to be bound by
the obligations of the Foundation under Section 3.1(g) and by this Section 3.3
with respect to the closing of such transaction and (ii) if the Company does not
accept the offer set forth in the Donee's Notice by written notice to the donee
during such five-Business Day period, to sell all of such Voting Securities on
the open market within 30 days following receipt of the Donation. If the Company
accepts the offer set forth in the Donee's Notice during such five-Business Day
period, the Company shall designate a closing date, time and place with respect
to such transaction in writing to the donee and, on such designated closing
date, pay to the donee the Purchase Price for all of the Voting Securities
received in the Donation by wire transfer of immediately available funds to an
account previously designated by the donee.

         Section 3.4 Designation of Purchaser. If the Company elects to exercise
a right of first refusal under this Article 3, the Company may specify in the
Company's Notice (or at any time thereafter which is prior to the purchase of
the Offered Shares to which such notice relates) another Person as its designee
to purchase such Offered Shares in accordance with the terms and provisions of
this Agreement. No such 



                                       5
<PAGE>   6
designation shall extend any of the time periods specified herein or change any
other term or provision hereof.

                                  ARTICLE FOUR

         Section 4.1 Covenants. During the Term the Foundation shall not, and
shall use its best efforts to cause each Person Controlled by it not to, singly
or as part of a Group, directly or indirectly:

                  (a) acquire, offer to acquire, or agree to acquire, by
         purchase, gift or otherwise, Beneficial Ownership of any Voting
         Securities, except (i) the Transfer Shares, (ii) pursuant to a stock
         split, stock dividend, rights offering, recapitalization,
         reclassification or similar transaction and (ii) for acquisitions that
         would not cause the aggregate Voting Power of the Voting Securities, on
         an issued and outstanding basis, Beneficially Owned by the Foundation
         to exceed 15% of the Total Voting Power;

                  (b) join or form a Group for the purpose of acquiring,
         holding, voting or disposing of any Voting Securities;

                  (c) deposit any Voting Securities into a voting trust or
         subject any Voting Securities to any arrangement or agreement with
         respect to the voting thereof; or

                  (d) pledge, hypothecate or otherwise encumber any Voting
         Securities, except as security for any loan the entire proceeds of
         which are used to make required distributions under Section 4942 of the
         Internal Revenue Code of 1986, as amended, and then only if the pledgee
         has theretofore agreed, pursuant to an instrument in form and substance
         satisfactory to the Company, to be bound by all of the terms and
         provisions of this Agreement to the same extent the Foundation is bound
         hereby.

         Section 4.2 Affirmative Covenants. Not withstanding any other term or
provision of this Agreement to the contrary, during the Term the Foundation
shall:

                  (a) comply with all applicable laws, rules and regulations
         relating to trading in securities while in the possession of material
         non-public information; and

                  (b) retain the name "Albertson" as part of its name, maintain
         its status as a charitable entity and associate the name "Albertson"
         with all charitable activities undertaken or otherwise participated in
         by the Foundation.

                                  ARTICLE FIVE

         Section 5.1 Representations and Warranties of the Company. The Company
represents and warrants to the Foundation as follows:



                                       6
<PAGE>   7
                  (a) The execution, delivery and performance by the Company of
         this Agreement and the consummation by the Company of the transactions
         contemplated by this Agreement are within the corporate powers of the
         Company and have been duly authorized by all necessary corporate action
         on the part of the Company. This Agreement constitutes a legal, valid
         and binding agreement of the Company enforceable against the Company in
         accordance with its terms (i) except as limited by applicable
         bankruptcy, insolvency, reorganization, moratorium or other similar
         laws now or hereafter in effect relating to or affecting creditors'
         rights generally, including the effect of statutory and other laws
         regarding fraudulent conveyances and preferential transfers, and (ii)
         subject to the limitations imposed by general equitable principles
         (regardless of whether such enforceability is considered in a
         proceeding at law or in equity).

                  (b) The execution, delivery and performance of this Agreement
         by the Company do not and will not contravene or conflict with or
         constitute a default under the Company's Restated Certificate of
         Incorporation or by-laws.

         Section 5.2 Representations and Warranties of the Foundation. The
Foundation represents and warrants to the Company as follows:

                  (a) The execution, delivery and performance by the Foundation
         of this Agreement and the consummation by the Foundation of the
         transactions contemplated by this Agreement are within the corporate
         powers of the Foundation and have been duly authorized by all necessary
         corporate action on the part of the Foundation. This Agreement
         constitutes a legal, valid and binding agreement of the Foundation
         enforceable against the Foundation in accordance with its terms (i)
         except as limited by applicable bankruptcy, insolvency, reorganization,
         moratorium or other similar laws now or hereafter in effect relating to
         or affecting creditors' rights generally, including the effect of
         statutory and other laws regarding fraudulent conveyances and
         preferential transfers, and (ii) subject to the limitations imposed by
         general equitable principles (regardless of whether such enforceability
         is considered in a proceeding at law or in equity).

                  (b) The execution, delivery and performance of this Agreement
         by the Foundation do not and will not contravene or conflict with or
         constitute a default under the Foundation's charter or by-laws.

                                   ARTICLE SIX

         Section 6.1  Enforcement; Consent to Jurisdiction.

                  (a) The Foundation and the Company acknowledge and agree that
         irreparable damage would occur if any of the provisions of this
         Agreement were not performed in accordance with their specific terms or
         were otherwise breached. Accordingly, the parties hereto agree that
         each party will be entitled to an injunction or injunctions to prevent
         breaches of this Agreement and to enforce specifically the provisions
         hereof, this being in addition to any other remedy to which either
         party may be entitled at law or in equity.

                  (b) The Company and the Foundation each irrevocably agrees
         that any legal action or proceeding to enforce this Agreement, or any
         claim or dispute arising out of or in connection 




                                       7
<PAGE>   8

         with, or in any way relating to, this Agreement or any transaction
         contemplated by this Agreement, shall be brought in the courts of the
         State of Idaho. By execution and delivery of this Agreement, the
         Company and the Foundation each irrevocably consents to submit itself
         to the jurisdiction of each such court and irrevocably designates,
         appoints and empowers the Secretary of State of the State of Idaho to
         receive for and on its behalf service of process in the State of Idaho.

         Section 6.2 No Waiver. Any waiver by either party hereto of any breach
of any provision of this Agreement shall not operate as or be construed to be a
waiver of any other breach of such provision or of any breach of any other
provision of this Agreement. The failure of either party hereto to insist upon
strict adherence to any term of this Agreement on one or more occasions shall
not be considered a waiver or deprive such party of the right thereafter to
insist upon strict adherence to such term or any other term of this Agreement.

         Section 6.3 Entire Agreement. This Agreement constitutes the entire
agreement and understanding of the parties hereto with respect to the subject
matter hereof and may be amended only by an agreement in writing executed by
each of the parties hereto.

         Section 6.4 Severability. If any provision of this Agreement is held by
a court of competent jurisdiction to be unenforceable, the remaining provisions
shall remain in full force and effect. It is declared to be the intention of the
parties hereto that they would have executed the remaining provisions without
including any provision that may be declared unenforceable.

         Section 6.5 Headings. Descriptive headings are for convenience only and
shall not control or affect the meaning or construction of any provision of this
Agreement.

         Section 6.6 Counterparts. For the convenience of the parties hereto,
any number of counterparts of this Agreement may be executed by the parties, and
each such executed counterpart shall be deemed an original instrument.

         Section 6.7 Notices. All notices, requests, demands and other
communications required or permitted hereunder shall be made in writing by
hand-delivery or by courier guaranteeing overnight delivery in accordance with
the following:

                  (a)      If to the Company, to:

                                    Thomas R. Saldin
                                    Executive Vice President, Administration
                                      and General Counsel
                                    Albertson's, Inc.
                                    250 East Parkcenter Boulevard
                                    Boise, Idaho 83706



                                       8
<PAGE>   9
                                    with a copy to:

                                    Kaye L. O'Riordan
                                    Corporate Secretary and Senior Attorney
                                    Albertson's, Inc.
                                    250 East Parkcenter Boulevard
                                    Boise, Idaho 83706

         or to such other person or address as the Company will furnish to the
         Foundation in writing.

                  (b)      If to the Foundation, to:

                                    J.A. and Kathryn Albertson Foundation, Inc.
                                    Suite 100
                                    380 East Parkcenter Boulevard
                                    Boise, Idaho 83706
                                    Attention:  Thomas J. Wilford

         or to such other person or address as the Foundation will furnish to
         the Company in writing.

                  (c) All notices, requests, demands and other communications
         given in accordance with this Section 6.7 shall be deemed to have been
         given for all purposes of this Agreement at the time of delivery by
         hand to the relevant office, if personally delivered, and on the next
         Business Day, if timely delivered to a courier guaranteeing overnight
         delivery.

         Section 6.8 Successors and Assigns. This Agreement shall bind the
successors and assigns of the parties hereto, and inure to the benefit of any
successor or permitted assign of either of them; provided, however, that no
party may assign this Agreement without the prior written consent of the other
party hereto, except that the Company may assign certain of its rights hereunder
in accordance with Section 3.4.

         Section 6.9 Governing Law. This Agreement shall be governed by and
construed and enforced in accordance with the internal laws of the State of
Idaho without giving effect to the conflict of laws principles thereof.

         Section 6.10  Legend.

                  (a) The share certificates evidencing Voting Securities
         Beneficially Owned by the Foundation during the Term shall bear the
         following legend until such time as such shares are free of the
         restrictions contained in this Agreement:

                  THE SHARES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO THE
                  PROVISIONS OF AN AGREEMENT, DATED AS OF ________], 1997,
                  BETWEEN ALBERTSON'S, INC. AND THE J.A. AND KATHRYN ALBERTSON
                  FOUNDATION AND MAY NOT BE SOLD OR TRANSFERRED EXCEPT IN
                  ACCORDANCE THEREWITH. A COPY OF SAID AGREEMENT IS ON FILE AT


                                       9
<PAGE>   10
                  THE OFFICE OF THE CORPORATE SECRETARY OF ALBERTSON'S, INC.

                  (b) The Foundation shall promptly present or cause to be
         presented to the Company all certificates representing shares Voting
         Securities now owned or hereafter acquired by the Foundation for the
         placement thereon of the legend provided for in this Section 6.10. The
         Company may enter a stop-transfer order with any transfer agent of the
         Voting Securities against transfer of such securities except in
         compliance with this Agreement. All legends and stop-transfer orders
         shall be removed with respect to any shares of Voting Securities that
         are sold, transferred or otherwise disposed of in accordance with the
         terms of this Agreement.

         Section 6.11 Non-Affected Shares. Notwithstanding any term or provision
of this Agreement to the contrary, the parties hereto acknowledge and agree that
the Foundation presently Beneficially Owns 1,180,000 shares of Common Stock (the
"Non-Affected Shares") and that no term or provision of this Agreement shall
apply to the Non-Affected Shares or to any Voting Securities acquired or issued
with respect to such Non-Affected Shares pursuant to any dividend reinvestment
plan or any stock split, stock or other dividend, rights offering,
recapitalization, reclassification or similar transaction.

         IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
executed by their duly authorized representatives as of the date first referred
to above.

                                     Albertson's, Inc.


                                     By: GARY G. MICHAEL
                                         -----------------      
                                         Name:  Gary G. Michael
                                         Title: Chairman of the Board and
                                                  Chief Executive Officer

                                     J.A. and Kathryn Albertson
                                       Foundation, Inc.


                                     By: J.B. SCOTT
                                         ------------
                                         Name:  J. B. Scott
                                         Title: President



                                       10