The goals of this study are to determine the following:

• To estimate the proportion of patients with a complete cytogenetic response (CCR) within each patient group
• To estimate the proportion of patients with a substantial molecular response (SMR) within each patient group
• To evaluate the frequency and severity of adverse events.
• To assess the feasibility of AG-858 production.

Inclusion Criteria:

• Must be Philadelphia chromosome positive chronic myelogenous leukemia in first chronic phase
• Must have a complete hematologic response
• Must have received Gleevec™, IFN-α, cytarabine, busulfan, hydroxyurea, Homoharringtonine (HHT) or any combination thereof as long as the combination has been discontinued and the dosing of Gleevec™ has been stable for 6 months or greater
• Must have one of the following cytogenetic statuses:

(A) Less than a CCR after receiving Gleevec™ for at least one year at a minimum dose of 400 mg/day. A stable dose of Gleevec™ must have been maintained for the last six months prior to eligibility testing OR (B) Stable cytogenetic status without CCR (no cytogenic response or progression) in three consecutive determinations over six months while on a stable dose of Gleevec™ (at a minimum of 400mg/day) for at least 6 months OR (C) Cytogenetic progression while on a stable dose of Gleevec™ (at a minimum dose of 400mg/day)for at least 2 consecutive evaluations at least one month apart

• ECOG performance score of 0 or 1
• Must be at least 18 years old
• Not pregnant or breastfeeding and agree to use contraception during the course of the study
• No prior allogeneic bone marrow transplant or be candidates for curative BMT
• No immunodeficiency or other serious illness
• No current use of immunosuppressive medications
• No other cancer within the last five years, with the exception of adequately treated cone-biopsied in situ carcinoma of the cervix uteri or basal or squamous cell carcinoma of the skin