Imatinib or Nilotinib With Pegylated Interferon-α2b in Chronic Myeloid Leukemia

Inclusion Criteria: * Patients must have a diagnosis of Philadelphia chromosome positive (Ph+) chronic myeloid leukemia in chronic phase by having met all of the following criteria at the time of their initial diagnosis: * Cytogenetic confirmation of Philadelphia chromosome or variants of the t(9;22) translocations. Patients may have secondary chromosomal abnormalities in addition to the Philadelphia chromosome. * Peripheral blood or bone marrow blast count \< 10%. * Peripheral blood basophil count \< 20%. * Platelet count ≥ 100,000 x 109/L. * If the peripheral blood counts are unavailable from the time of their original diagnosis, but there is no evidence of accelerated- or blast-phase disease from prior clinical or other medical records, then they will be allowed to participate. * Patients must be eighteen years of age or older. * Patients must be actively receiving treatment for their CML with a a tyrosine kinase inhibitor, either imatinib or nilotinib. * Patients may be receiving imatinib mesylate. Patients must be on imatinib mesylate for a minimum of 2 years, and be on a stable dose for at least one consecutive year leading up to enrollment. * Patients may be receiving nilotinib (Tasigna) as frontline therapy or as second line therapy if the reason for the switch from imatinib to nilotinib was intolerance to imatinib. Patients cannot have been switched from imatinib to nilotinib because of a concern or demonstration for resistance to frontline imatinib. Patients must be on nilotinib for a minimum of 2 years, and be on a stable does for at least one consecutive year leading up to enrollment. * Patients must have an ongoing complete hematologic response (CHR) on a a TKI (imatinib or nilotinib), defined as follows: * WBC ≤ 10 x 109/L. * Platelet count \< 450,000 x 109/L. * No blasts or promyelocytes in peripheral blood. * No evidence of disease-related symptoms and extramedullary disease, including the liver and spleen. * Patients must have a complete cytogenetic response (CCyR) on a TKI (imatinib or nilotinib) for a minimum of 1 year leading up to enrollment. Complete cytogenetic response is defined as 0% Ph+ cells in metaphase, in the bone marrow and/or a negative peripheral blood FISH analysis for the Bcr-Abl gene fusion, and an ongoing CCyR must be confirmed by bone marrow aspirate cytogenetics and/or peripheral blood FISH for Bcr-Abl within 4 weeks of starting treatment. * Patients may have a negative quantitative RT-PCR (qPCR) for BCR-ABL at the time of enrollment, but if the qPCR is positive, patients cannot have greater than 1% bcr-ABl / Abl /ABL transcript, present in 2 consecutive qPCR analyses, performed at least 3 months apart, in the 6 to 12 months leading up to enrollment. * Patients must have an ECOG performance status of 0-2 (Appendix 13.1). * All patients must be informed of the investigational nature of this study and standard alternative therapy. All patients must sign and give written informed consent in accordance with institutional and federal guidelines. Exclusion Criteria: * Patients who have had prior progression of their CML to accelerated phase or blast crisis. * Patients who have previously undergone hematopoietic stem cell transplantation. * Patients who have previously been treated with interferon-α. * Patients with an absolute neutrophil count (ANC) \< 1500/mm3 and/or a platelet count \< 100,000/mm3. * Patients with serum bilirubin, SGOT\[AST\], SGPT\[ALT\], or serum creatinine \> 1.5 x the upper limit of normal (ULN). * Patients with an INR or PTT \> 1.5 x ULN, with the exception of patients on treatment with oral anticoagulants. * Patients with uncontrolled medical diseases such as diabetes mellitus, neuropsychiatric disorders, infection, angina, severe hypertension, pulmonary disease (chronic obstructive pulmonary disease \[COPD\] with hypoxemia), major organ malfunction (liver, kidney) or class III or IV cardiac disease as defined by the New York Heart Association Criteria. * Patients who are (a) pregnant, (b) breast feeding, (c) of childbearing potential without a negative pregnancy test prior to Study Day 1, and (d) male or female of childbearing potential unwilling to use barrier contraceptive precautions throughout the trial (postmenopausal women must be amenorrheic for at least 12 months to be considered of non-childbearing potential). * Patients with a history of another active malignancy within the last five years, which required treatment with chemotherapy, hormonal therapy, or radiation therapy. Exceptions to this rule include basal cell and squamous cell skin carcinomas or cervical carcinoma in situ. * Patients with a history of non-compliance to medical regimens or who are considered potentially unreliable.