<PAGE>   1
                                                                    EXHIBIT 4.05



        THE SECURITIES REPRESENTED BY THIS WARRANT HAVE NOT BEEN REGISTERED
        UNDER THE SECURITIES ACT OF 1933 OR QUALIFIED UNDER APPLICABLE STATE
        SECURITIES LAWS, 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
        SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION AND QUALIFICATION ARE
        NOT REQUIRED.


WARRANT NO.  CG-1                                DATE OF ISSUANCE: April 8, 1999


                           WARRANT TO PURCHASE SHARES
                               OF COMMON STOCK OF

                               CORIXA CORPORATION


        This Warrant is issued to Castle Gate, L.L.C., a Washington limited
liability company ("Purchaser") pursuant to that certain Equity Line of Credit
and Securities Purchase Agreement dated as of April 8, 1999 between Corixa
Corporation, a Delaware corporation ("Corixa" or the "Company"), and Purchaser
(the "Purchase Agreement") and is subject to the terms and conditions therein.

        1.     EXERCISE OF WARRANT.

              (a) Method of Exercise. Subject to the terms and conditions herein
set forth, upon surrender of this Warrant at the principal office of Corixa and
upon payment of the purchase price by wire transfer to Corixa or cashiers check
drawn on a United States bank made to the order of Corixa, or exercise of the
right to credit the Warrant Price (as defined in Section 1(d)) against the fair
market value of the Warrant Stock (as defined below) at the time of exercise
(the "Net Exercise Right") pursuant to Section 1(b), Purchaser is entitled to
purchase from Corixa, at any time following the occurrence of an event set forth
in Subsections 1(c)(i)-(iii) respectively, and on or before the ten (10) year
anniversary of an event set forth in Subsections 1(c)(i)-(iii), respectively,
that number of fully paid and non-assessable shares of Corixa Common Stock, par
value $0.001 per share ("Warrant Stock") set forth in such Subsections
1(c)(i)-(iii), respectively, upon the occurrence of such event. Subject to
adjustment as hereinafter provided, the purchase price of one share of Warrant
Stock (or such securities as may be substituted for one share of Warrant Stock
pursuant to the provisions hereinafter set forth) shall be the Warrant Price.

              (b) Net Exercise Right. If the Company shall receive written
notice from the holder of this Warrant at the time of exercise of this Warrant
that the holder elects to exercise


<PAGE>   2

Purchaser's Net Exercise Right, Corixa shall deliver to such holder (without
payment by the Purchaser of any exercise price of any cash or other
consideration ) that number of shares of fully paid and nonassessable Common
Stock equal to the quotient obtained by dividing (x) the value of this Warrant
(or the specified portion thereof) on the date of exercise, which value shall be
determined by subtracting (1) the aggregate Warrant Price of the Warrant Stock
immediately prior to the exercise of this Warrant from (2) the aggregate fair
market value of the Warrant Stock issuable upon exercise of this Warrant (or
specified portion thereof) on the date of exercise by (y) the fair market value
of one share of Common Stock on the date of exercise. For purposes of this
Section 1(b), "fair market value" of a share of Common Stock shall mean the
closing price of the Common Stock on the business day prior to the date of
exercise as reported by the Nasdaq National Market or such other principal
exchange or quotation system on which the Common Stock is then traded. For
purposes of this Warrant, shares issued pursuant to the Net Exercise Right shall
be treated as if they were issued upon the exercise of this Warrant.

              (c) Number of Shares Subject to Warrant. Subject to Section 1(a),
this Warrant is exercisable for:

                     (i) up to 250,000 shares of Common Stock at any time on or
        after the date Corixa and Purchaser enter into the Purchase Agreement;

                     (ii) up to 62,500 shares at any time upon or after the
        consummation of the Initial Draw (as that term is defined in the
        Purchase Agreement); and

                     (iii) upon each Subsequent Draw (as defined in the Purchase
        Agreement) consummated by the Company in accordance with the Purchase
        Agreement, up to that number of shares equal to the product obtained by
        multiplying (x) 250,000 by (y) a fraction, the numerator of which is the
        amount of such Subsequent Draw and the denominator of which is
        $50,000,000, at any time effective after such Subsequent Draw; provided,
        however, that in no event will this Warrant be exercisable for greater
        than an aggregate of 187,500 shares of Common Stock under this
        Subsection 1(c)(iii).

               (d) Price of Shares Subject to Warrant. The "Warrant Price" shall
be equal to (i) in the case of Subsections 1(c)(i) and 1(c)(ii), $8.50 per share
and (ii) in the case of Subsection 1(c)(iii), the average per share closing
price of Corixa Common Stock on the Nasdaq National Market as reported in the
Wall Street Journal for the period beginning sixty (60) days before the date the
Subsequent Draw is consummated and ending sixty (60) days after the date the
Subsequent Draw is consummated (or such shorter period during which Corixa
shares are traded if Corixa shares shall for any reason cease to be publicly
traded).

        2.     CERTAIN ADJUSTMENTS.

              (a) Mergers or Consolidations. If at any time after the date
hereof there shall be a capital reorganization (other than a combination or
subdivision of Warrant Stock otherwise provided for herein), or a merger or
consolidation of Corixa with another corporation (other than a merger with
another corporation in which Corixa is a continuing corporation and which does
not result in any reclassification or change of outstanding securities issuable
upon exercise of this



                                     - 2 -
<PAGE>   3

Warrant), then, as a part of such reorganization, merger or consolidation,
lawful provision shall be made so that Purchaser shall thereafter be entitled to
receive upon exercise of this Warrant, during the period specified in this
Warrant and upon payment of the Warrant Price, the number of shares of stock or
other securities or property of Corixa or the successor corporation resulting
from such reorganization, merger or consolidation, to which a holder of the
Common Stock deliverable upon exercise of this Warrant would have been entitled
under the provisions of the agreement in such reorganization, merger or
consolidation if this Warrant had been exercised immediately before that
reorganization, merger or consolidation. In any such case, appropriate
adjustment (as determined in good faith by Corixa's Board of Directors) shall be
made in the application of the provisions of this Warrant with respect to the
rights and interests of Purchaser after the reorganization, merger or
consolidation to the end that the provisions of this Warrant (including
adjustment of the Warrant Price then in effect and the number of shares of
Warrant Stock) shall be applicable after that event, as near as reasonably may
be, in relation to any shares or other property deliverable after that event
upon exercise of this Warrant.

               (b) Splits and Subdivisions; Dividends. In the event Corixa
should at any time or from time to time fix a record date for the effectuation
of a split or subdivision of the outstanding shares of Common Stock or the
determination of the holders of Common Stock entitled to receive a dividend or
other distribution payable in additional shares of Common Stock or other
securities or rights convertible into, or entitling the holder thereof to
receive directly or indirectly, additional shares of Common Stock (hereinafter
referred to as the "Common Stock Equivalents") without payment of any
consideration by such holder for the additional shares of Common Stock or Common
Stock Equivalents (including the additional shares of Common Stock issuable upon
conversion or exercise thereof), then, as of such record date (or the date of
such distribution, split or subdivision if no record date is fixed), the per
share Warrant Price shall be appropriately decreased and the number of shares of
Warrant Stock shall be appropriately increased in proportion to such increase
(or potential increase) of outstanding shares.

               (c) Combination of Shares. If the number of shares of Common
Stock outstanding at any time after the date hereof is decreased by a
combination of the outstanding shares of Common Stock, the per share Warrant
Price shall be appropriately increased and the number of shares of Warrant Stock
shall be appropriately decreased in proportion to such decrease in outstanding
shares.

               (d) Adjustments for Other Distributions. In the event Corixa
shall declare a distribution payable in securities of other persons, evidences
of indebtedness issued by Corixa or other persons, assets (excluding cash
dividends paid out of net profits) or options or rights not referred to in
Section 2(b), then, in each such case for the purpose of this Section 2(d), upon
exercise of this Warrant the holder hereof shall be entitled to a proportionate
share of any such distribution as though such holder was the holder of the
number of shares of Common Stock of Corixa into which this Warrant may be
exercised as of the record date fixed for the determination of the holders of
Common Stock of Corixa entitled to receive such distribution.

        3. NO FRACTIONAL SHARES. No fractional shares of Warrant Shares will be
issued in connection with any exercise of this Warrant. In lieu of any
fractional shares which would



                                     - 3 -
<PAGE>   4

otherwise be issuable, Corixa shall pay cash equal to the product of such
fraction multiplied by the closing price of one Warrant Share as reported on the
Nasdaq National Market on the date of exercise.

        4. NO STOCKHOLDER RIGHTS. Until the exercise of this Warrant or any
portion of this Warrant, Purchaser shall not have nor exercise any rights by
virtue hereof as a stockholder of Corixa (including without limitation the right
to notification of stockholder meetings or the right to receive any notice or
other communication concerning the business and affairs of Corixa).

        5. RESERVATION OF STOCK. Corixa covenants that during the period this
Warrant is exercisable, Corixa will reserve from its authorized and unissued
Common Stock a sufficient number of shares of Common Stock (or other securities,
if applicable) to provide for the issuance of Warrant Stock (or other
securities) upon the exercise of this Warrant. Corixa agrees that its issuance
of this Warrant shall constitute full authority to its officers who are charged
with the duty of executing stock certificates to execute and issue the necessary
certificates for the Warrant Stock upon the exercise of this Warrant.

        6.     EXERCISE OF WARRANT.

               (a) Procedural Requirements. Subject to Section 6(b), this
Warrant may be exercised by the holder hereof, in whole or in part, by the
surrender of this Warrant and the Notice of Exercise attached hereto as Exhibit
A duly completed and executed on behalf of the holder hereof, at the principal
office of Corixa together with payment in full of the Warrant Price then in
effect with respect to the number of shares of Warrant Stock as to which the
Warrant is being exercised. The Warrant Price shall be paid by wire transfer to
Corixa or cashiers check drawn on a United States bank made to the order of
Corixa or by exercise of the Net Exercise Right pursuant to Section 1(b). This
Warrant shall be deemed to have been exercised immediately prior to the close of
business on the date of its surrender for exercise as provided above, and the
person entitled to receive the Warrant Stock issuable upon such exercise shall
be treated for all purposes as the holder of such shares of record as of the
close of business on such date. As promptly as practicable on or after such date
and in any event within twenty (20) days thereafter, Corixa at its expense shall
cause to be issued and delivered to the person or persons entitled to receive
the same a certificate or certificates for the number of full shares of Warrant
Stock issuable upon such exercise, together with cash in lieu of any fraction of
a share as provided above. The shares of Warrant Stock issuable upon exercise
hereof shall, upon their issuance, be fully paid and nonassessable. In the event
that this Warrant is exercised in part, Corixa at its expense will execute and
deliver a new Warrant of like tenor exercisable for the number of shares for
which this Warrant may then be exercised.

               (b) Hart-Scott-Rodino. Prior to any exercise of this Warrant, the
Company and the Purchaser shall consult with each other pursuant to Section 5(d)
of the Purchase Agreement as to whether any applications and/or documents may be
required to be executed and filed under the Hart-Scott-Rodino Antitrust
Improvements Act of 1976, as amended ("HSR") in connection with such exercise
and shall mutually agree on an appropriate cause of action with respect to the
foregoing. In the event the Company and the Purchaser mutually agree that the



                                     - 4 -
<PAGE>   5

filing of applications and/or documents are required under HSR, then no exercise
of this Warrant shall take place until the expiration or early termination of
any notice periods required under HSR with respect to the filing of such
applications and/or documents.

        7. CERTIFICATE OF ADJUSTMENT. Whenever the Warrant Price or number or
type of securities issuable upon exercise of this Warrant is adjusted, as herein
provided, Corixa shall, at its expense, promptly deliver to the record holder of
this Warrant a certificate of an officer of Corixa setting forth the nature of
such adjustment and showing in detail the facts upon which such adjustment is
based.

        8. REPRESENTATIONS OF PURCHASER. As of the date hereof, Purchaser hereby
confirms the representations and warranties made by Purchaser in Section 3 of
the Purchase Agreement.

        9. TRANSFER RESTRICTIONS.

               (a) UNREGISTERED SECURITY. The 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 "1933 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 1933 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 Corixa, 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) NO TRANSFER. This Warrant is not transferable without the
Company's prior written consent; provided, however, such consent shall not be
required in connection with the transfer by the Purchaser of such Warrant (but
only with all related obligations) to (i) an Affiliate of the Purchaser (as such
term is defined in the Standstill Agreement dated as of April 8, 1999 between
the Company and the Purchaser), (ii) an entity solely in connection with
charitable contributions by the Purchaser or (iii) an individual or entity
solely for estate planning purposes, provided that (x) written notice (in the
form of Exhibit B as attached hereto) is provided to the Company at least five
(5) business days prior to any such transfer, (y) a minimum of 5,000 shares of
Warrant Stock are transferred in each instance, and (z) immediately following
such transfer the further disposition of such Warrant Stock by the transferee is
restricted under the 1933 Act and the transferee agrees in writing to be bound
by all of the provisions of this Warrant.

        10. NOTICES OF RECORD DATE. In the event of:

               (a) any taking by Corixa of a record of the holders of any class
of securities for the purpose of determining the holders thereof who are
entitled to receive any dividend (other than a cash dividend payable out of
earned surplus of Corixa) or other distribution, or any right to



                                     - 5 -
<PAGE>   6

subscribe for, purchase or otherwise acquire any shares of stock of any class or
any other securities or property, or to receive any other right; or

               (b) any capital reorganization of Corixa, any reclassification or
recapitalization of the capital stock of Corixa or any transfer of all or
substantially all the assets of Corixa to or consolidation or merger of Corixa
with or into any other person; or

               (c) any voluntary or involuntary dissolution, liquidation or
winding-up of Corixa,

               then and in each such event Corixa will mail or cause to be
mailed to the holder of this Warrant a notice specifying (i) the date on which
any such 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, and (ii) the date on which any such reorganization, reclassification,
recapitalization, transfer, consolidation, merger, dissolution, liquidation or
winding-up is to take place, and the time, if any, as of which the holders of
record of Common Stock (or other securities) shall be entitled to exchange their
shares of Common Stock (or other securities) for securities or other property
deliverable upon such reorganization, reclassification, recapitalization,
transfer, consolidation, merger, dissolution, liquidation or winding-up. Such
notice shall be mailed at least 10 days prior to the date therein specified.

        11. REPLACEMENT OF WARRANTS. On receipt of evidence reasonably
satisfactory to Corixa of the loss, theft, destruction or mutilation of this
Warrant and, in the case of any such loss, theft, destruction or mutilation of
this Warrant, on delivery of an indemnity agreement or security reasonably
satisfactory in form and amount to Corixa or, in the case of any such
mutilation, on surrender and cancellation of such Warrant, Corixa at its expense
will execute and deliver, in lieu thereof, a new Warrant of like tenor.

        12.    MARKET STANDOFF.

               (a) Purchaser hereby agrees that, during the period of duration
(up to, but not exceeding, 90 days) specified by Corixa and an underwriter of
Common Stock or other securities of Corixa, following the effective date of a
registration statement of Corixa filed under the 1933 Act, it shall not, to the
extent requested by Corixa and such underwriter, directly or indirectly sell,
offer to sell, contract to sell (including, without limitation, any short sale),
grant any option to purchase or otherwise transfer or dispose of (other than to
donees who agree to be similarly bound) any securities of Corixa held by it at
any time during such period except Common Stock included in such registration.

               (b) In order to enforce the foregoing covenant, Corixa may impose
stop-transfer instructions with respect to the securities held by Purchaser
until the end of such period, and Purchaser agrees that, if so requested,
Purchaser will execute an agreement in the form provided by the underwriter
containing terms which are essentially consistent with the provisions of this
Section 12.



                                     - 6 -
<PAGE>   7

        13. NO IMPAIRMENT. Corixa 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 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.

        14. TERMINATION. This Warrant (and the right to purchase Warrant Stock
upon exercise hereof) shall terminate as to the right to purchase that number of
Warrant Stock set forth in Subsections 1(c)(i)-(iii), respectively, upon the
date that is the ten (10) year anniversary of the occurrence of the applicable
event set forth in Subsections 1(c)(i)-(iii), respectively.

        15. SATURDAYS, SUNDAYS, HOLIDAYS, ETC. If the last or appointed day for
the taking of any action or the expiration of any right required or granted
herein shall be a Saturday or Sunday or shall be a legal holiday, then such
action may be taken or such right may be exercised on the next succeeding day
not a Saturday, Sunday or legal holiday.

        16. EXCHANGE ACT FILINGS. Purchaser agrees and acknowledges that it
shall have sole responsibility for making any filings with the U.S. Securities
and Exchange Commission pursuant to Sections 13 and 16 of the Securities
Exchange Act of 1934, as amended, as a result of its acquisition of this Warrant
and the Warrant Stock (collectively, the "Securities") and any future retention
or transfer thereof.

        17. NO LEGAL, TAX OR INVESTMENT ADVICE. Purchaser understands that
nothing in this Agreement or any other materials presented to Purchaser in
connection with the acquisition of the Securities constitutes legal, tax or
investment advice. Purchaser has consulted such legal, tax and investment
advisors as it, in its sole discretion, has deemed necessary or appropriate in
connection with its acquisition of the Securities.

        18. MISCELLANEOUS. This Warrant shall be governed by the laws of the
State of Washington. The headings in this Warrant are for purposes of
convenience and reference only, and shall not be deemed to constitute a part
hereof. Neither this Warrant nor any term hereof may be changed, waived,
discharged or terminated orally but only by an instrument in writing signed by
Corixa and the Purchaser. All notices and other communications from Corixa to
the holder of this Warrant shall be sufficient if in writing and sent by
registered or certified mail, domestic or international courier, or facsimile,
return receipt requested, postage or courier charges prepaid, to the address
furnished to Corixa in writing by Purchaser. All such notices and communications
shall be effective if delivered (i) personally, (ii) by facsimile transmission
(receipt verified), (iii) by registered or certified mail (return receipt
requested), postage prepaid, or (iv) sent by express courier service (receipt
verified), and if to Purchaser, with a copy to Mark Beatty, Preston Gates &
Ellis, 701 Fifth Avenue, #5000, Seattle, Washington 98104, and if to Corixa,
with a copy to William W. Ericson, Venture Law Group, 4750 Carillon Point,
Kirkland, Washington 98033. The invalidity or unenforceability of any provision
hereof shall in no way affect the validity or enforceability of any other
provisions.



                                     - 7 -
<PAGE>   8

        IN WITNESS WHEREOF, this Common Stock Purchase Warrant is issued
effective as of this 8th day of April, 1999.


                                        CORIXA CORPORATION



                                        By: /s/ Steven Gillis
                                            ------------------------------------
                                            Steven Gillis
                                            Chairman and Chief Executive Officer


                                        ACKNOWLEDGED AND AGREED:

                                        CASTLE GATE, L.L.C.



                                        By: /s/ MICHAEL LARSON
                                            ------------------------------------

                                        Name:    Michael Larson
                                              ----------------------------------

                                        Title:   Business Manager
                                               ---------------------------------



                        SIGNATURE PAGE TO THE WARRANT TO
                         PURCHASE SHARES OF COMMON STOCK

<PAGE>   9

                                    EXHIBIT A


                          NOTICE OF INTENT TO EXERCISE
                  (To be signed only upon exercise of Warrant)



To:   CORIXA CORPORATION

The undersigned, the Holder of the within Warrant, hereby irrevocably elects to
exercise the purchase right represented by such Warrant for, and to purchase
thereunder, _____________ ____________________________ (_____________) shares of
Common Stock of Corixa Corporation and (choose one)

       ___  herewith makes payment of ____________________ Dollars ($__________)
thereof

or
       ___ exercises Holder's Net Exercise Right pursuant to Section 1(b)
thereof .


and requests that the certificates for such shares be issued in the name of, and
delivered to ________________________________, whose address is ________________
________________________________________________________________________________
_____________________________.


DATED: ______________



                                        ________________________________________
                                        (Signature must conform in all respects
                                        to name of Holder as specified on the
                                        face of the Warrant)


                                        ________________________________________

                                        ________________________________________
                                        (Address)


<PAGE>   10

                                    EXHIBIT B

                            NOTICE OF 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, to:

<TABLE>
<CAPTION>
     NAME OF ASSIGNEE               ADDRESS/FAX NUMBER           NO. OF SHARES
     ----------------               ------------------           -------------
<S>                                 <C>                          <C>

</TABLE>




Dated:_________________                     Signature:

                                            Witness: