Ruxolitinib in Combination With Nilotinib in Chronic Myeloid Leukemia (CML) Patients

Inclusion Criteria: * Must have chronic phase chronic myeloid leukemia (CML). They must also be under treatment with nilotinib as either first, second, or third-line therapy. * Must have a complete cytogenetic response (CCyR) OR must have been on nilotinib for a minimum of 6 months. * Must not have undergone treatment for any other form of cancer (aside from non-melanoma skin cancer) in the past 5 years. * 18 years of age or older and must be able to speak and read English or Spanish. * Able to provide informed consent. * Prior therapy with a tyrosine kinase inhibitor (TKI) other than nilotinib is allowable, however, nilotinib must be the current therapy. All participants must be under the care of a Moffitt Cancer Center physician, and enrollment is expected to be complete within 6 months. * Eastern Cooperative Oncology Group (ECOG) performance status ≤2 (Karnofsky ≥60%. * Must have normal organ and marrow function as defined in study protocol. * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of Ruxolitinib and nilotinib administration. Women of child-bearing age will be required to have a negative pregnancy test within 14 days of enrolling in this study. * Ability to understand and the willingness to sign a written informed consent document * B-HCG will be performed on all women of child-bearing potential as screening prior to enrollment on this trial. STAT3 levels in the bone marrow will also be measured prior to enrollment. Exclusion Criteria: * Patients who are in accelerated phase or blast phase CML. * May not be receiving any other investigational agents. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ruxolitinib or other agents used in the study. * Known history of a prolonged QT interval (QTc \>480). * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant women are excluded from this study. Women who are breast feeding their infants should discontinue this practice if the mother is treated with ruxolitinib. * Currently receiving any drugs considered to be strong CYP3A4 inducers or inhibitors which cannot be discontinued or changed to an alternative drug prior to enrolling on the trial. * HIV-positive patients receiving combination anti-retroviral therapy are excluded from the study. * Patients receiving nilotinib 200 mg by mouth, twice a day (PO BID) or a lower dose are not eligible.