EXHIBIT 99.1

         Geron Corporation Announces Exercise of Over-Allotment Option

    MENLO PARK, Calif.--(BUSINESS WIRE)--Nov. 5, 2003--Geron
Corporation (Nasdaq:GERN) today announced that the underwriters of its
recent public offering of 5,000,000 shares of common stock have
exercised their over-allotment option in full to purchase 750,000
additional shares, resulting in gross proceeds of $9 million.
    UBS Securities LLC acted as the sole book-running manager in this
offering. SG Cowen Securities Corporation, Lazard and Needham &
Company, Inc. were co-managers.
    This press release does not constitute an offer to sell or the
solicitation of an offer to buy any of these securities. A copy of the
final prospects and related base prospectus is available from UBS
Securities LLC, ECMG Syndicate, 299 Park Avenue, New York, New York
10171.
    Geron is a biopharmaceutical company focused on developing and
commercializing therapeutic and diagnostic products for cancer based
on its telomerase technology, and cell-based therapeutics using its
human embryonic stem cell technology.

    This news release may contain forward-looking statements made
pursuant to the "safe harbor" provisions of the Private Securities
Litigation Reform Act of 1995. Investors are cautioned that such
forward-looking statements in this press release constitute
forward-looking statements involving risks and uncertainties,
including, without limitation, risks inherent in the development and
commercialization of potential products, reliance on collaborators,
need for additional capital, need for regulatory approvals or
clearances, and the maintenance of our intellectual property rights.
Actual results may differ materially from the results anticipated in
these forward-looking statements. Additional information on potential
factors that could affect our results and other risks and
uncertainties are detailed from time to time in Geron's periodic
reports, including the quarterly report on Form 10-Q for the quarter
ended on June 30, 2003.


    CONTACT: Geron Corporation
             David L. Greenwood, 650-473-7765