<PAGE>

                                                                       EXHIBIT 4

                                                                  CONFORMED COPY

                    AMENDMENT NO. 1 dated as of July 23, 1999 (this
               "Amendment"), between ARCH CHEMICALS, INC., a Virginia
               corporation (the "Company") and FIRST CHICAGO TRUST COMPANY OF
               NEW YORK, as Rights Agent ("First Chicago"), to Rights Agreement
               dated as of January 29, 1999 (the "Rights Agreement"), between
               the Company and ChaseMellon Shareholder Services, L.L.C.
               ("ChaseMellon").


          WHEREAS the Company and ChaseMellon entered into the Rights Agreement
on January 29, 1999;

          WHEREAS the Company has removed ChaseMellon as Rights Agent under the
Rights Agreement by delivering written notice of such removal in accordance with
Section 22 of the Rights Agreement, and the Company desires to appoint First
Chicago as Rights Agent under the Rights Agreement; and

          WHEREAS the Company, pursuant to Section 26 of the Rights Agreement,
has determined to amend the Rights Agreement as set forth herein.

          NOW THEREFORE, in consideration of the mutual premises and the mutual
agreements set forth herein, the parties hereby agree as follows:

          SECTION 1.  Appointment of New Rights Agent.
                      -------------------------------
Pursuant to and in accordance with Section 22 of the Rights Agreement, the
Company hereby appoints First Chicago as Rights Agent under the Rights
Agreement, and First Chicago hereby accepts such appointment. Without any
further action, First Chicago shall be the Rights Agent under the Rights
Agreement, and shall succeed to all of the covenants, agreements, obligations,
rights and benefits of ChaseMellon in its former capacity as Rights Agent under
the Rights Agreement (as amended hereby).

          SECTION 2.  Section 3.  Section 3(d) of the Rights Agreement is hereby
                      ----------
amended as follows:

          (a) By deleting the words "ChaseMellon Shareholder Services, L.L.C."
in the first sentence of the legend set forth therein and replacing such words
with the words "First Chicago Trust Company of New York";
<PAGE>

                                                                               2

          (b)  By deleting the words "Rights Agent" in the third sentence of the
legend set forth therein and replacing such words with the word "Company"; and

          (c)  By deleting the last sentence thereof and replacing it with the
following sentence:

          "Notwithstanding this paragraph (d), neither the omission of a legend
          (or any words thereof), nor the inclusion of a different legend or a
          legend that makes reference to a rights agreement other than the
          Rights Agreement shall affect the enforceability of any part of this
          Rights Agreement or the rights of any holder of the Rights."

          SECTION 3.  Section 22.  Section 22 of the Rights Agreement is hereby
                      -----------
amended by deleting the fifth sentence thereof and replacing it with the
following sentence:

          "Any successor Rights Agent, whether appointed by the Company or by
          such a court, shall be (A) a Person organized and doing business under
          the laws of the United States or of any state of the United States, in
          good standing, having a principal office in the United States, which
          is subject to supervision or examination by Federal or state authority
          and which has (either alone or together with an Affiliate) at the time
          of its appointment as Rights Agent a combined capital and surplus of
          at least $25,000,000 or (B) an Affiliate of a Person described in
          clause (A) of this sentence; provided that the principal transfer
                                       --------
          agent for the Common Shares shall in any event be qualified to be the
          Rights Agent."

          SECTION 4.  Section 25.  Section 25 of the Rights Agreement is hereby
                      -----------
amended by deleting the name and address of ChaseMellon and replacing it with
the following:

          "First Chicago Trust Company of New York
          525 Washington Blvd.
          Suite 4660
          Jersey City, NJ 07310
          Attention:  Corporate Actions Administration".
<PAGE>

                                                                               3

          SECTION 5.  Section 26.  Section 26 of the Rights Agreement is hereby
                      -----------
amended by deleting the word "last" in the first sentence thereof and replacing
such word with the word "penultimate".

          SECTION 6.  Exhibit B.  Exhibit B of the Rights Agreement is hereby
                      ----------
amended by deleting the words "ChaseMellon Shareholder Services, L.L.C., a New
Jersey corporation" and "CHASEMELLON SHAREHOLDER SERVICES, L.L.C." and replacing
such words with the words "First Chicago Trust Company of New York" and "FIRST
CHICAGO TRUST COMPANY OF NEW YORK", respectively.

          SECTION 7.  Certain References.  (a)  All references in the Rights
                      -------------------
Agreement (and in any exhibits thereto) to the "Rights Agent" shall be deemed to
be references to First Chicago.

          (b)  All references in the Rights Agreement (and in any exhibits
thereto) to the term "Rights Agreement" or to the terms "herein", "hereof" or
words of similar import shall in each case be deemed to be references to the
Rights Agreement as amended hereby.

          SECTION 8.  Rights Agreement.  Except as expressly amended hereby, the
                      -----------------
Rights Agreement shall remain in full force and effect, and shall be otherwise
unaffected hereby.

          SECTION 9.  Governing Law.  This Amendment shall be deemed to be a
                      --------------
contract made under the law of the Commonwealth of Virginia and for all purposes
shall be governed by and construed in accordance with the law of such
Commonwealth applicable to the contracts to be made and performed entirely
within such Commonwealth.

          SECTION 10. Severability.  If any term, provision, covenant or
                      -------------
restriction of this Amendment is held by a court of competent jurisdiction or
other authority to be invalid, void or unenforceable, the remainder of the
terms, provisions, covenants and restrictions of this Amendment shall remain in
full force and effect and shall in no way be affected, impaired or invalidated.
<PAGE>

                                                                               4

          SECTION 11. Counterparts; Effectiveness.  This Amendment may be
                      ----------------------------
executed in any number of counterparts and each of such counterparts shall for
all purposes be deemed to be an original, and all such counterparts shall
together constitute one and the same instrument.  This Amendment shall be
effective as of 5:00 p.m. New York City time on July 23, 1999.


          IN WITNESS WHEREOF, the parties hereto have caused this Amendment to
be duly executed as of the day and year first above written.

                         ARCH CHEMICALS, INC.,

                         by
                            /s/ Michael E. Campbell
                            -------------------------------------
                            Name:  Michael E. Campbell
                            Title: Chairman of the Board and
                                   Chief Executive Officer


                         FIRST CHICAGO TRUST COMPANY
                         OF NEW YORK, as Rights Agent,

                         by
                            /s/ Michael S. Duncan
                            -------------------------------------
                            Name:  Michael S. Duncan
                            Title: Director, Corporate Actions