Inclusion Criteria:

1. Patients with Ph chromosome positive or BCR-ABL-positive CML (as determined by cytogenetics, FISH, or RT-PCR).
2. Patients must have reached their 18th birthday.
3. Patients must have received imatinib therapy for at least 12 months and must not have had changes in their dose of imatinib in the last 6 months. Patients must not have had a continuous interruption of imatinib therapy of greater than 14 days or for a total of 6 weeks in the 6 months prior to enrollment.
4. Patients must be in complete cytogenetic remission confirmed by two marrows, the second being at least one month after the first.
5. Patients must have detectable BCR-ABL transcript levels that are not more than 0.5-log lower than the lowest value obtained in the last 6 months, with at least two values obtained during this period.
6. Karnofsky performance status should be > 70.
7. Adequate organ function defined as: bilirubin <2x upper limit of normal (ULN), creatinine <1.5x ULN, and ALT and AST <2.5x ULN.
8. All patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines.
9. Women of childbearing potential (i.e., not post-menopausal 24 months or not surgically sterile) must agree to use effective methods of contraception.

Exclusion Criteria:

1. Patients with a history of accelerated or blast crisis. Accelerated phase is defined as 15 to 30% blasts or >30% blasts plus promyelocytes in the peripheral blood or marrow, >20% basophils, or platelets <100 x 10^9/L, unrelated to therapy. Cytogenetic abnormalities in addition to the Ph chromosome are not considered a defining feature of accelerated phase.
2. Patients with autoimmune disorders or known immune deficiency.
3. Patients receiving immunosuppressive therapy, corticosteroids, chemotherapy, or therapy for CML other than imatinib.
4. Patients receiving any other investigational agents.
5. Patients who are pregnant or breast-feeding.
6. Patients with clinically significant heart disease (New York Heart Association Class III or IV) or other serious intercurrent illnesses, active uncontrolled infections requiring antibiotics or active bleeding.
7. Patients who have undergone major surgery within 28 days before registration, or who have not fully recovered from any other prior major surgery.
8. Patients who have undergone stem cell transplantation.
9. Patients who have received radiation therapy within 4 weeks of enrollment.