<PAGE>


                                                                     Exhibit 4.4

THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AND HAVE BEEN ACQUIRED FOR INVESTMENT AND NOT WITH A
VIEW TO, OR IN CONNECTION WITH, THE SALE OR DISTRIBUTION THEREOF.  NO SUCH SALE
OR DISTRIBUTION MAY BE EFFECTED WITHOUT AN EFFECTIVE REGISTRATION STATEMENT
RELATED THERETO OR AN OPINION OF COUNSEL IN A FORM SATISFACTORY TO THE COMPANY
THAT SUCH REGISTRATION IS NOT REQUIRED UNDER THE SECURITIES ACT OF 1933.
--------------------------------------------------------------------------------

Warrant No. CS-4                                 Number of Shares:  25,000
Date of Issuance: July 27, 1999             (subject to adjustment)

                             Chemdex Corporation

                        Common Stock Purchase Warrant
                        -----------------------------

     Chemdex Corporation (the "Company"), for value received, hereby certifies
                               -------
that ALZA Corporation, or its registered assigns (the "Registered Holder"), is
                                                       -----------------
entitled, subject to the terms set forth below, to purchase from the Company, at
any time after the date hereof and on or before the Expiration Date (as defined
in Section 5 below), up to 25,000 shares (as adjusted from time to time pursuant
to the provisions of this Warrant) of Common Stock of the Company, at a purchase
price of $15.00 per share.  The shares purchasable upon exercise of this Warrant
and the purchase price per share, as adjusted from time to time pursuant to the
provisions of this Warrant, are sometimes hereinafter referred to as the
"Warrant Stock" and the "Purchase Price," respectively.
 -------------           --------------

     This Warrant is non-forfeitable and issued pursuant to a Warrant Purchase
Agreement dated July 27, 1999 between the Company and the Registered Holder (the
"Purchase Agreement") and is subject to the terms and conditions of the Purchase
 ------------------
Agreement.

     1.  Exercise.
         --------

          (a) Manner of Exercise.  Subject to the provisions of subsection 1(e)
              ------------------
below, this Warrant may be exercised by the Registered Holder at any time after
the issuance of this Warrant, in whole or in part, by surrendering this Warrant,
with the purchase form appended hereto as Exhibit A duly executed by such
                                          ---------
Registered Holder or by such Registered Holder's duly authorized attorney, at
the principal office of the Company, or at such other office or agency as the
Company may designate, accompanied by payment in full of the Purchase Price
payable in respect of the number of shares of Warrant Stock purchased upon such
exercise.  The Purchase Price may be paid by cash, check, wire transfer or by
the surrender of promissory notes or other instruments representing indebtedness
of the Company to the Registered Holder.

          (b) Effective Time of Exercise.  Each exercise of this Warrant shall
              --------------------------
be deemed to have been effected immediately prior to the close of business on
the day on which this Warrant shall have been surrendered to the Company as
provided in Section 1(a) above.  At such time, the person or persons in whose
name or names any certificates for Warrant Stock shall be issuable upon such
exercise as provided in Section 1(d) below shall be deemed to have become the
holder or holders of record of the Warrant Stock represented by such
certificates.
<PAGE>

          (c)  Net Issue Exercise.
               ------------------

               (i) In lieu of exercising this Warrant in the manner provided
above in Section 1(a), the Registered Holder may elect to receive shares equal
to the value of this Warrant (or the portion thereof being canceled) by
surrender of this Warrant at the principal office of the Company together with
notice of such election in which event the Company shall issue to holder a
number of shares of Common Stock computed using the following formula:

               X =              Y (A - B)
                                ---------
                                    A
Where     X = The number of shares of Common Stock to be issued to the
              Registered Holder.

          Y = The number of shares of Common Stock purchasable under this
              Warrant (at the date of such calculation).

          A = The fair market value of one share of Common Stock (at the date of
              such calculation).

          B = The Purchase Price (as adjusted to the date of such calculation).

               (ii) For purposes of this Section 1(c), the fair market value
of one share of Common Stock on the date of calculation shall mean:

                    (A) if the Company's Common Stock is traded on a
securities exchange or The Nasdaq Stock Market or actively traded over-the-
counter:

                        (1) if the Company's Common Stock is traded on a
securities exchange or The Nasdaq Stock Market, the fair market value shall be
deemed to be the average of the closing prices over the three (3) trading-day
period ending the trading day before date of calculation; or

                        (2) if the Company's Common Stock is actively traded
over-the-counter, the fair market value shall be deemed to be the average of
the closing bid or sales price (whichever is applicable) over the three (3)
trading-day period ending the trading day before the date of calculation; or

                    (B) if (A) is not applicable, the fair market value shall
be at the highest price per share which the Company could obtain on the date
of calculation from a willing buyer (not a current employee or director) for
shares of Common Stock sold by the Company, from authorized but unissued
shares, as determined in good faith by the Board of Directors, unless the
Company is at such time subject to an acquisition as described in Section 6(b)
below, in which case the fair market value per share of Common Stock shall be
deemed to be the value of the consideration per share received by the holders
of such stock pursuant to such acquisition.

          (d) Delivery to Holder.  As soon as practicable after the exercise of
              ------------------
this Warrant in whole or in part, and in any event within ten (10) days
thereafter, the Company at its expense will cause to be issued in the name of,
and delivered to, the Registered Holder, or as such Holder (upon payment by such
Holder of any applicable transfer taxes) may direct:

                                      -2-
<PAGE>

              (i) a certificate or certificates for the number of shares of
Warrant Stock to which such Registered Holder shall be entitled, and

              (ii) in case such exercise is in part only, a new warrant or
warrants (dated the date hereof) of like tenor, calling in the aggregate on
the face or faces thereof for the number of shares of Warrant Stock equal
(without giving effect to any adjustment therein) to the number of such shares
called for on the face of this Warrant minus the number of such shares
purchased by the Registered Holder upon such exercise as provided in Section
1(a) above.

     2.  Adjustments.
         -----------

          (a)  Stock Splits and Dividends.  If outstanding shares of the
               --------------------------
Company's Common Stock shall be subdivided into a greater number of shares or a
dividend in Common Stock shall be paid in respect of Common Stock, the Purchase
Price in effect immediately prior to such subdivision or at the record date of
such dividend shall simultaneously with the effectiveness of such subdivision or
immediately after the record date of such dividend be proportionately reduced.
If outstanding shares of Common Stock shall be combined into a smaller number of
shares, the Purchase Price in effect immediately prior to such combination
shall, simultaneously with the effectiveness of such combination, be
proportionately increased.  When any adjustment is required to be made in the
Purchase Price, the number of shares of Warrant Stock purchasable upon the
exercise of this Warrant shall be changed to the number determined by dividing
(i) an amount equal to the number of shares issuable upon the exercise of this
Warrant immediately prior to such adjustment, multiplied by the Purchase Price
in effect immediately prior to such adjustment, by (ii) the Purchase Price in
effect immediately after such adjustment.

          (b) Reclassification, Etc.  In case of any reclassification or change
              ----------------------
of the outstanding securities of the Company or of any reorganization of the
Company (or any other corporation the stock or securities of which are at the
time receivable upon the exercise of this Warrant) or any consolidation or
merger by the Company with another entity or the conveyance of all or
substantially all of the Company's assets, or any similar corporate
reorganization on or after the date hereof, then and in each such case the
holder of this Warrant, upon the exercise hereof at any time after the
consummation of such reclassification, change, reorganization, merger or
conveyance, shall be entitled to receive, in lieu of the stock or other
securities and property receivable upon the exercise hereof prior to such
consummation, the stock or other securities or property to which such holder
would have been entitled upon such consummation if such holder had exercised
this Warrant immediately prior thereto, all subject to further adjustment as
provided in Section 2(a); and in each such case, the terms of this Section 2
shall be applicable to the shares of stock or other securities properly
receivable upon the exercise of this Warrant after such consummation.

          (c) Adjustment Certificate. When any adjustment is required to be made
              ----------------------
in the Warrant Stock or the Purchase Price pursuant to this Section 2, the
Company shall promptly mail to the Registered Holder a certificate setting forth
(i) a brief statement of the facts requiring such adjustment, (ii) the Purchase
Price after such adjustment and (iii) the kind and amount of stock or other
securities or property into which this Warrant shall be exercisable after such
adjustment.

     3.  Limitations on Transfer.  In addition to any other limitation on
         -----------------------
transfer created by applicable securities laws, the Registered Holder shall
not assign, encumber or dispose of any interest except in compliance with the
provisions below and applicable securities laws.

                                      -3-
<PAGE>

          (a) Unregistered Security.  Each holder of this Warrant acknowledges
              ---------------------
that this Warrant and the Warrant Stock have not been registered under the
Securities Act of 1933, as amended (the "Securities Act"), and agrees not to
                                         --------------
sell, pledge, distribute, offer for sale, transfer or otherwise dispose of this
Warrant or any Warrant Stock issued upon its exercise in the absence of (i) an
effective registration statement under the Act as to this Warrant or such
Warrant Stock and registration or qualification of this Warrant or such Warrant
Stock under any applicable U.S. federal or state securities law then in effect
or (ii) an opinion of counsel, satisfactory to the Company, that such
registration and qualification are not required.  Each certificate or other
instrument for Warrant Stock issued upon the exercise of this Warrant shall bear
a legend substantially to the foregoing effect.

          (b) Transferability. Subject to the provisions of Section 3(a) hereof,
              ---------------
this Warrant and all rights hereunder are transferable, in whole or in part,
upon surrender of the Warrant with a properly executed assignment (in the form
of Exhibit B hereto) at the principal office of the Company; provided, however,
   ---------                                                 --------  -------
that this Warrant may not be transferred in part unless the transferee acquires
the right to purchase at least 10,000 shares (as adjusted pursuant to Section 2)
of Warrant Stock hereunder.

          (d) Warrant Register.   The Company will maintain a register
              ----------------
containing the names and addresses of the Registered Holders of this Warrant.
Until any transfer of this Warrant is made in the warrant register, the Company
may treat the Registered Holder of this Warrant as the absolute owner hereof for
all purposes; provided, however, that if this Warrant is properly assigned in
              --------  -------
blank, the Company may (but shall not be required to) treat the bearer hereof as
the absolute owner hereof for all purposes, notwithstanding any notice to the
contrary.  Any Registered Holder may change such Registered Holder's address as
shown on the warrant register by written notice to the Company requesting such
change.

     4.  No Impairment.  The Company will not, by amendment of its charter or
         -------------
through reorganization, consolidation, merger, dissolution, sale of assets or
any other voluntary action, avoid or seek to avoid the observance or performance
of any of the terms of this Warrant, but will (subject to Section 13 below) at
all times in good faith assist in the carrying out of all such terms and in the
taking of all such action as may be necessary or appropriate in order to protect
the rights of the holder of this Warrant against impairment.

     5.  Termination.  This Warrant (and the right to purchase securities upon
         -----------
exercise hereof) shall terminate upon  the fifth anniversary of the date of this
Warrant (the "Expiration Date").
              ---------------

     6.  Notices of Certain Transactions.  In case:
         -------------------------------

          (a) the Company shall take a record of the holders of its Common Stock
(or other stock or securities at the time deliverable upon the exercise of this
Warrant) for the purpose of entitling or enabling them to receive any dividend
or other distribution, or to receive any right to subscribe for or purchase any
shares of stock of any class or any other securities, or to receive any other
right, to subscribe for or purchase any shares of stock of any class or any
other securities, or to receive any other right, or

          (b) of any capital reorganization of the Company, any reclassification
of the capital stock of the Company, any consolidation or merger of the Company,
any consolidation or merger of the Company with or into another corporation
(other than a consolidation or merger in which the Company is the surviving
entity), or any transfer of all or substantially all of the assets of the
Company, or

                                      -4-
<PAGE>

          (c) of the voluntary or involuntary dissolution, liquidation or
winding-up of the Company,

then, and in each such case, the Company will mail or cause to be mailed to the
Registered Holder of this Warrant a notice specifying, as the case may be, (i)
the date on which a record is to be taken for the purpose of such dividend,
distribution or right, and stating the amount and character of such dividend,
distribution or right, or (ii) the effective date on which such reorganization,
reclassification, consolidation, merger, transfer, dissolution, liquidation or
winding-up is to take place, and the time, if any is to be fixed, as of which
the holders of record of Common Stock (or such other stock or securities at the
time deliverable upon such reorganization, reclassification, consolidation,
merger, transfer, dissolution, liquidation or winding-up) are to be determined.
Such notice shall be mailed at least ten (10) days prior to the record date or
effective date for the event specified in such notice.

     7.  Reservation of Stock.  The Company will at all times reserve and keep
         --------------------
available, solely for the issuance and delivery upon the exercise of this
Warrant, such shares of Warrant Stock and other stock, securities and property,
as from time to time shall be issuable upon the exercise of this Warrant.

     8.  Exchange of Warrants.  Upon the surrender by the Registered Holder of
         --------------------
the Warrant, properly endorsed, to the Company at the principal office of the
Company, the Company will, subject to the provisions of Section 3 hereof, issue
and deliver to or upon the order of such Holder, at the Company's expense, a new
Warrant of like tenor, in the name of such Registered Holder or as such
Registered Holder (upon payment by such Registered Holder of any applicable
transfer taxes) may direct, calling in the aggregate on the face or faces
thereof for the number of shares of Common Stock called for on the face of the
Warrant so surrendered.

     9.  Replacement of Warrants.  Upon receipt of evidence reasonably
         -----------------------
satisfactory to the Company of the loss, theft, destruction or mutilation of
this Warrant and (in the case of loss, theft or destruction) upon delivery of an
indemnity agreement (with surety if reasonably required) in an amount reasonably
satisfactory to the Company, or (in the case of mutilation) upon surrender and
cancellation of this Warrant, the Company will issue, in lieu thereof, a new
Warrant of like tenor.

     10.  Notices.  Any notice required or permitted by this Warrant shall be in
          -------
writing and shall be deemed sufficient upon receipt, when delivered personally
or by courier, overnight delivery service or confirmed facsimile, or forty-eight
(48) hours after being deposited in the regular mail as certified or registered
mail (airmail if sent internationally) with postage prepaid, addressed (a) if to
the Registered Holder, to the address of the Registered Holder most recently
furnished in writing to the Company and (b) if to the Company, to the address
set forth below or subsequently modified by written notice to the Registered
Holder.

     11.  No Rights as Stockholder.  Until the exercise of this Warrant, the
          ------------------------
Registered Holder of this Warrant shall not have or exercise any rights by
virtue hereof as a stockholder of the Company.

     12.  No Fractional Shares.  No fractional shares of Common Stock will be
          --------------------
issued in connection with any exercise hereunder.  In lieu of any fractional
shares which would otherwise be issuable, the Company shall pay cash equal to
the product of such fraction multiplied by the fair market value of one share of
Common Stock on the date of exercise, as determined in good faith by the
Company's Board of Directors.

                                      -5-
<PAGE>

     13.  Amendment or Waiver.  Any term of this Warrant may be amended or
          -------------------
waived only by an instrument in writing signed by the party against which
enforcement of the amendment or waiver is sought.

     14.  Headings.  The headings in this Warrant are for purposes of reference
          --------
only and shall not limit or otherwise affect the meaning of any provision of
this Warrant.

     15.  Governing Law. This Warrant shall be governed, construed and
          -------------
interpreted in accordance with the laws of the State of California, without
giving effect to principles of conflicts of law.

                                      -6-
<PAGE>

                              Chemdex Corporation

                              By:
                                 ----------------------------------------
                                 David P. Perry
                                 President and Chief Executive Officer

                              Address:  3950 Fabian Way
                                        Palo Alto, CA 94303

                              Fax Number:  (650) 813-0304

AGREED AND ACCEPTED:

ALZA CORPORATION

By:
   -------------------------------

Name:
     -----------------------------

Title:
      ----------------------------

Address:

Fax Number:

               SIGNATURE PAGE TO COMMON STOCK PURCHASE WARRANT
<PAGE>

                                  EXHIBIT A
                                  ---------

                                PURCHASE FORM
                                -------------

To:  Chemdex Corporation                                    Dated:

     The undersigned, pursuant to the provisions set forth in the attached
Warrant No. CS-4, hereby irrevocably elects to purchase _______ shares of the
Common Stock covered by such Warrant and herewith makes payment of $_________,
representing the full purchase price for such shares at the price per share
provided for in such Warrant.

     The undersigned acknowledges that it has reviewed the representations and
warranties contained in subsections 3(b)-(f) of the Purchase Agreement (as
defined in the Warrant) and by its signature below hereby makes such
representations and warranties to the Company.  Defined terms contained in such
representations and warranties shall have the meanings assigned to them in the
Purchase Agreement, provided that the term "Purchaser" shall refer to the
                    --------
undersigned and the term "Securities" shall refer to the Warrant Stock.

     The undersigned further acknowledges that it has reviewed the market
standoff provisions set forth in Section 6 of the Purchase Agreement and agrees
to be bound by such provisions.

                                    Signature:
                                              -------------------------------

                                    Name (print):
                                                 ----------------------------

                                    Title (if applic.)
                                                      -----------------------

                                    Company (if applic.):
                                                         --------------------
<PAGE>

                                  EXHIBIT B
                                  ---------

                               ASSIGNMENT FORM
                               ---------------

     FOR VALUE RECEIVED, _________________________________________ hereby sells,
assigns and transfers all of the rights of the undersigned under the attached
Warrant with respect to the number of shares of Common Stock covered thereby set
forth below, unto:

<TABLE>
<CAPTION>
          Name of Assignee                      Address/Fax Number                  No. of Shares
          ----------------                      ------------------                  -------------
<S>                                   <C>                                      <C>



</TABLE>

Dated:                           Signature:
      --------------                       -------------------------

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

                                 Witness:
                                           -------------------------