<PAGE>   1
                                                                   EXHIBIT 10.10

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. PD-1                              Date of Issuance: December 7, 2000
80,000 shares

                              XCYTE THERAPIES, INC.

                    SERIES D PREFERRED STOCK PURCHASE WARRANT

        Xcyte Therapies, Inc. (the "Company"), for value received, hereby
certifies that Hibbs/Woodinville Associates LLC, 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 80,000 shares of
Series D Preferred Stock of the Company ("Preferred Stock"), at a purchase price
of $2.78 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 hereinafter referred to as the "Warrant Stock"
and the "Purchase Price," respectively.



        1.     EXERCISE.

               (a) MANNER OF EXERCISE. This Warrant may be exercised by the
Registered Holder, in whole or in part, by surrendering this Warrant, with the
purchase/exercise 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.

               (c)    NET ISSUE EXERCISE.

<PAGE>   2

                      (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 on the purchase/exercise form appended
hereto as Exhibit A duly executed by such Registered Holder or such Registered
Holder's duly authorized attorney, in which event the Company shall issue to
such Holder a number of shares of Warrant Stock computed using the following
formula:

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

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

               A = The fair market value of one share of Warrant 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 Warrant Stock on the date of calculation shall mean with respect to
each share of Warrant Stock:

                             (A) if the exercise is in connection with an
initial public offering of the Company's Common Stock, and if the Company's
Registration Statement relating to such public offering has been declared
effective by the Securities and Exchange Commission, then the fair market value
per share shall be the product of (x) the initial "Price to Public" specified in
the final prospectus with respect to the offering and (y) the number of shares
of Common Stock into which each share of Warrant Stock is convertible at the
date of calculation;

                             (B) if (A) is not applicable, the fair market value
of Warrant Stock 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 Warrant 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 of Warrant Stock shall
be deemed to be the value 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:

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


                                      -2-
<PAGE>   3

                      (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) or 1(c)
above.

        2. ADJUSTMENTS.

           (a) REDEMPTION OR CONVERSION OF PREFERRED STOCK. If all of the
Preferred Stock is redeemed or converted into shares of Common Stock, then this
Warrant shall automatically become exercisable for that number of shares of
Common Stock equal to the number of shares of Common Stock that would have been
received if this Warrant had been exercised in full and the shares of Preferred
Stock received thereupon had been simultaneously converted into shares of Common
Stock immediately prior to such event, and the Exercise Price shall be
automatically adjusted to equal the number obtained by dividing (i) the
aggregate Purchase Price of the shares of Preferred Stock for which this Warrant
was exercisable immediately prior to such redemption or conversion, by (ii) the
number of shares of Common Stock for which this Warrant is exercisable
immediately after such redemption or conversion.

           (b) STOCK SPLITS AND DIVIDENDS. If outstanding shares of the
Company's Preferred Stock shall be subdivided into a greater number of shares or
a dividend in Preferred Stock shall be paid in respect of Preferred 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 Preferred 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.

           (c) RECLASSIFICATION, ETC. In case there occurs 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 similar corporate
reorganization on or after the date hereof, then and in each such case the
Registered Holder, upon the exercise hereof at any time after the consummation
of such reclassification, change, or reorganization 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 pursuant to the provisions of this Section 2.


                                      -3-
<PAGE>   4

           (d) 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.

           (e) ACKNOWLEDGEMENT. In order to avoid doubt, it is acknowledged that
the holder of this Warrant shall be entitled to the benefit of all adjustments
in the number of shares of Common Stock of the Company issuable upon conversion
of the Preferred Stock of the Company which occur prior to the exercise of this
Warrant, including without limitation, any increase in the number of shares of
Common Stock issuable upon conversion as a result of a dilutive issuance of
capital stock.

        3. TRANSFERS.

           (a) UNREGISTERED SECURITY. Each holder of this Warrant acknowledges
that this Warrant, the Warrant Stock and the Common Stock of the Company 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, any Warrant Stock issued upon its
exercise or any Common Stock issued upon conversion of the Warrant Stock in the
absence of (i) an effective registration statement under the Act as to this
Warrant, such Warrant Stock or such Common Stock and registration or
qualification of this Warrant, such Warrant Stock or such Common 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 to any individual
or entity with the consent of the Company, which consent shall not be
unreasonably withheld; provided that any assignee shall be bound by the terms
hereof. Notwithstanding the foregoing, this Warrant may not be transferred to
any individual or entity engaged in any business that competes with any business
of the Company, and any purported transfer to a such an individual or entity
shall be void. A permitted transfer of this Warrant shall be effected by
surrendering the Warrant with a properly executed assignment (in the form of
Exhibit B hereto) at the principal office of the Company. This Warrant may not
be transferred in part unless the transferee acquires the right to purchase all
of the shares of Warrant Stock hereunder.

           (c) 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


                                      -4-
<PAGE>   5

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. REPRESENTATIONS AND WARRANTIES OF HOLDER.  The Registered Holder
hereby represents and warrants to the Company as follows:

           (a) PURCHASE ENTIRELY FOR OWN ACCOUNT. The Registered Holder
acknowledges that this Warrant is given to the Registered Holder in reliance
upon the Registered Holder's representation to the Company, which by its
acceptance of this Warrant the Registered Holder hereby confirms, that the
Warrant, the Warrant Shares, and the Common Stock issuable upon conversion of
the Warrant Shares (collectively, the "Securities") being acquired by the
Registered Holder are being acquired for investment for the Registered Holder's
own account, not as a nominee or agent, and not with a view to the resale or
distribution of any part thereof, and that the Registered Holder has no present
intention of selling, granting any participation in, or otherwise distributing
the same. By executing this Agreement, the Registered Holder further represents
that the Registered Holder does not presently have any contract, undertaking,
agreement or arrangement with any person to sell, transfer or grant
participations to such person or to any third person, with respect to any of the
Securities. The Registered Holder represents that it has full power and
authority to enter into this Agreement. The Registered Holder has not been
formed for the specific purpose of acquiring any of the Securities.

           (b) DISCLOSURE OF INFORMATION. The Registered Holder has had an
opportunity to discuss the Company's business, management, financial affairs and
the terms and conditions of the offering of the Securities with the Company's
management and has had an opportunity to review the Company's facilities. The
Registered Holder understands that such discussions, as well as the written
information issued by the Company, were intended to describe the aspects of the
Company's business which it believes to be material.

           (c) RESTRICTED SECURITIES. The Registered Holder understands that the
Securities have not been, and will not be, registered under the Securities Act,
by reason of a specific exemption from the registration provisions of the
Securities Act which depends upon, among other things, the bona fide nature of
the investment intent and the accuracy of the Registered Holder's
representations as expressed herein. The Registered Holder understands that the
Securities are "restricted securities" under applicable U.S. federal and state
securities laws and that, pursuant to these laws, the Registered Holder must
hold the Securities indefinitely unless they are registered with the Securities
and Exchange Commission and qualified by state authorities, or an exemption from
such registration and qualification requirements is available. The Registered
Holder further acknowledges that if an exemption from registration or
qualification is available, it may be conditioned on various requirements
including, but not limited to, the time and manner of sale, the holding period
for the Securities, and on requirements relating to the Company which are
outside of the Registered Holder's control, and which the Company is under no
obligation and may not be able to satisfy.


                                      -5-
<PAGE>   6

           (d) NO PUBLIC MARKET. The Registered Holder understands that no
public market now exists for any of the securities issued by the Company, that
the Company has made no assurances that a public market will ever exist for the
Securities.

           (e) LEGENDS. The Registered Holder understands that the Securities,
and any securities issued in respect of or exchange for the Securities, may bear
one or all of the following legends:

               (i) "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 DISPOSITION 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."

               (ii) Any legend required by the Blue Sky laws of any state to the
extent such laws are applicable to the shares represented by the certificate so
legended.

           (f) ACCREDITED INVESTOR. The Registered Holder is an accredited
investor as defined in Rule 501(a) of Regulation D promulgated under the Act.

        5. 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 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.

        6. TERMINATION. This Warrant (and the right to purchase securities upon
exercise hereof) shall terminate upon the earliest to occur of the following
(the "Expiration Date"): (a) January 20, 2006, (b) within 20 business days of
the sale, conveyance or disposal of all or substantially all of the Company's
property or business or the Company's merger into or consolidation with any
other corporation (other than a wholly-owned subsidiary of the Company) or
within 20 business days of any other transaction or series of related
transactions in which more than fifty percent (50%) of the voting power of the
Company is disposed of, provided that this Section 6(b) shall not apply to a
merger effected exclusively for the purpose of changing the domicile of the
Company, or (c) the closing of a firm commitment underwritten public offering
pursuant to a registration statement on FORM S-1 under the Securities Act, the
public offering price of which is not less than $4.00 per share (appropriately
adjusted for any stock split, dividend, combination or other recapitalization)
and which results in aggregate cash proceeds to the Company of $20,000,000 (net
of underwriting discounts and commissions).


                                      -6-
<PAGE>   7

        7. NOTICES OF CERTAIN TRANSACTIONS. In case:

           (a) the Company shall take a record of the holders of its Preferred
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

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

           (d) of any redemption of the Preferred Stock or mandatory conversion
of the Preferred Stock into Common Stock of the Company, or

           (e) of a public offering described in Section 6(c).

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, (ii) the effective date on which such reorganization,
reclassification, consolidation, merger, transfer, dissolution, liquidation,
winding-up, redemption or conversion is to take place, and the time, if any is
to be fixed, as of which the holders of record of Preferred Stock (or such other
stock or securities at the time deliverable upon such reorganization,
reclassification, consolidation, merger, transfer, dissolution, liquidation,
winding-up, redemption or conversion) are to be determined, or (iii) the
expected date on which the closing of a firm commitment underwritten public
offering described in Section 6(c) shall occur. 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.

        8. 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.

        9. EXCHANGE OF WARRANTS. Upon the surrender by the Registered Holder of
any Warrant or Warrants, 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 or Warrants of like tenor, in the name of such Registered
Holder or as such Registered Holder (upon payment by such Registered


                                      -7-
<PAGE>   8

Holder of any applicable transfer taxes) may direct, calling in the aggregate on
the face or faces thereof for the number of shares of Preferred Stock called for
on the face or faces of the Warrant or Warrants so surrendered.

        10. 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.

        11. MAILING OF NOTICES. Any notice required or permitted pursuant to
this Warrant shall be in writing and shall be deemed sufficient upon receipt,
when delivered personally or sent 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.

        12. 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.

        13. NO FRACTIONAL SHARES. No fractional shares of Preferred 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
Preferred Stock on the date of exercise, as determined in good faith by the
Company's Board of Directors.

        14. 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.

        15. 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.

        16. GOVERNING LAW. This Warrant shall be governed, construed and
interpreted in accordance with the laws of the State of Washington, without
giving effect to principles of conflicts of law.

        17. INVESTOR RIGHTS AGREEMENT. The Warrant Stock and any Common Stock
issued upon conversion of the Warrant Stock shall be deemed "Registrable
Securities" under the Amended and Restated Investor Rights Agreement dated as of
May 25, 2000, as amended, between the Company, the Investors identified therein
to the fullest extent possible, and the Registered Holder shall be deemed, and
become to the fullest extent possible by virtue of the issuance of this Warrant,
a "Holder" under said Agreement, entitled to all of the registration and


                                      -8-
<PAGE>   9

other rights, benefits and privileges accorded "Holders" thereunder to the
fullest extent possible, and subject to all obligations, duties and conditions
imposed on "Holders" thereunder to the fullest extent possible. The Registered
Holder, the Warrant, the Warrant Stock and any common stock issued upon
conversion of the Warrant Stock shall be subject to the "market standoff"
obligations pursuant to Section 1.14 of said Agreement. The Company's Board of
Directors acting pursuant to Section 1.13(ii) of said Agreement shall grant to
Registered Holder to the fullest extent possible all registration rights
accorded Holders thereunder.


                                      -9-
<PAGE>   10

                                      XCYTE THERAPIES, INC.


                                      By
                                        ------------------------------------

                                      Address:    1124 Columbia Street
                                                  Suite 130
                                                  Seattle, WA  98104

                                      Fax Number: (206) 262-0900



                        SIGNATURE PAGE TO XCYTE THERAPIES
                          WARRANT TO PURCHASE SERIES D
                       TO HIBBS/WOODINVILLE ASSOCIATES LLC

<PAGE>   11

                                    EXHIBIT A

                             PURCHASE/EXERCISE FORM


To:     XCYTE THERAPIES, INC.                                    Dated:

        The undersigned, pursuant to the provisions set forth in the attached
Warrant No. PD-1, hereby irrevocably elects to (a) purchase _____ shares of the
Preferred 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, or (b) exercise such Warrant for _______ shares
purchasable under the Warrant pursuant to the Net Issue Exercise provisions of
Section 1(c) of such Warrant.

        The undersigned further acknowledges that it has reviewed the
representations and warranties of the Registered Holder contained in Section 4
of the Warrant and the covenants of the Registered Holder contained in Section
17 of the Warrant, and by its signature below the undersigned hereby makes such
representations, warranties and covenants to the Company as of the date hereof.


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

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

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

                              Company (if applic.):
                                                   ------------------

<PAGE>   12
                                    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 Series D Preferred
Stock covered thereby set forth below, unto:

NAME OF ASSIGNEE            ADDRESS/FAX NUMBER              NO. OF SHARES






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

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

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