Treatment Free Remission After Combination Therapy With Ruxolitinib Plus Tyrosine Kinase Inhibitors

Inclusion Criteria: * Willing and able to give informed consent * Diagnosed with CML in chronic phase and have either the b3a2 (e14a2) or b2a2 (e13a2) variants that give rise to the p210 BCR-ABL protein. * Must have a documented history of attempting only one prior TKI discontinuation under the guidance of a treating physician * Must have met ALL the following criteria prior to first attempt to discontinue their TKI: * Stable molecular response (MR4; \<0.01% IS) for \> 2 years (allowance for a 2 week variance), as documented on at least 4 tests, performed at least 3 months apart. If any results are \>0.05% IS, tests must have been repeated within 1 month and be less than 0.01% IS and stable. * Treatment with one of the following FDA approved TKI; imatinib, dasatinib, nilotinib or bosutinib, at any dose for a minimum of approximately 3 years (allowance of a 4 week variance) prior to discontinuing TKIs * Has been on any number of TKIs, but has not been resistant to any TKI (changes made for intolerance are allowed) * Must have relapsed (defined as loss of major molecular response (MMR), RQ-PCR for BCR-ABL \> 0.1% IS after first attempted discontinuation of TKI * After first failed TFR attempt, must have a minimum duration of 1 year on a TKI, and must plan to remain on this same TKI for a minimum of 12 months during the combination treatment phase * Current TKI must be the same as the TKI being taken prior to the initial TFR attempt (e.g., if patient is on imatinib prior to first TFR attempt, they should be on imatinib at time of enrollment on this study) * Eastern Cooperative Oncology Group (ECOG) performance status 0-3 * Must have a RQ-PCR for BCR-ABL less than 0.0032% IS (MR4.5) reported by the trial designated central lab at time of study enrollment * Must adhere to all study contraception guidelines Exclusion Criteria: * History of accelerated or blast phase CML * History of TKI resistance * A second malignancy requiring active treatment * Have previously received treatment with a JAK inhibitor. * Platelet count less than 100 × 10\^9/L or an absolute neutrophil count of less than 1 × 10\^9/L or Hemoglobin less than 8 g/dL * AST and ALT ≥ 3 times the institutional upper limit of normal (ULN) * Creatinine ≥ 2 times ULN * Total bilirubin ≥ 1.5 times ULN or \>3.0 x the ULN with Gilbert Syndrome (unless direct bilirubin is within normal limits) * Pregnant or lactating * Unable to comply with lab appointments schedule and patient response outcome assessments * Another investigational drug within 4 weeks of enrollment * Any serious medical or psychiatric illness that could, in the investigator's opinion, interfere with the completion of treatment according to this protocol * Have undergone a prior allogeneic transplant * Screening 12-lead ECG showing a baseline corrected QT interval \>500msec (patients with a pacemaker will still be eligible with QTc\>500msec)