To investigate whether patients with chronic-phase chronic myeloid leukemia (CP-CML) who have achieved a complete cytogenetic response (CCyR) on imatinib (IM) or nilotinib (N) can then be treated with a combination of the tyrosine kinase inhibitor (TKI) and interferon-α2b (PEG-IFN-a2b, [IFN]) for 2 years, subsequently have their therapy discontinued, and then maintain a durable molecular response off all therapy. Relapse-free survival (RFS) rate 1 year after discontinuation of the TKI and IFN will be the measurement of this objective.