Inclusion Criteria:

          -  Patients with Philadelphia chromosome (Ph)-positive or BCR/ABL-positive CML (as
             determined by cytogenetics, FISH, or PCR).

          -  Patients must be on continuous TKI therapy for management of their CML. Any
             commercially available and FDA- approved TKI can be used, i.e., imatinib mesylate
             (IM), nilotinib (NIL) or dasatinib (DAS). Patients may be receiving TKI at entry in
             the frontline or salvage setting, including patients currently on imatinib after
             alpha-interferon failure or on dasatinib or nilotinib after failure to prior therapy
             including imatinib.

          -  Patients must have received the current TKI for at least 18 months and not have
             increased their dose in the last 6 months.

          -  For the phase I portion of the study, patients may be included without a CCyR provided
             they remain in chronic or accelerated phase CML and have at least a complete
             hematologic response (CHR). For the Phase II portion of the study patients must be in
             complete cytogenetic remission (CCyR), regardless of the stage of disease they had at
             the time they started therapy with TKI.

          -  Patients must have detectable BCR-ABL transcript levels meeting at least 1 of the
             following criteria: Patient has never achieved a major molecular response (MMR, as
             defined by a BCR-ABL/ABL =< 0.1% in the international scale (currently equivalent to
             0.28 in the MD Anderson Cancer Center [MDACC] molecular diagnostic laboratory), and
             transcript levels have shown in at least 2 consecutive measures separated by at least
             1 month to have increased by any value; or achieved a major molecular response which
             has been lost, with an interim increase in transcript levels by at least one-log,
             confirmed in two consecutive analyses separated by at least 1 month; or patient has
             received therapy for at least 2 years & lacks a sustained major molecular response; or
             patient has received therapy for at least 5 years and lacks a sustained complete
             molecular response (CMR, defined as transcript levels still detectable in the MDACC
             molecular diagnostic laboratory).

          -  Patients must not have had a known interruption of TKI therapy of greater than 21
             consecutive days or for a total of 6 weeks in the 6 months prior to enrollment.

          -  Patients must be able to understand and sign an informed consent indicating that they
             are aware of the investigational nature of this study in keeping with the
             institutional policies.

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2.

          -  Bilirubin < 2 x upper limit of normal (ULN) (unless associated with Gilbert's
             syndrome).

          -  Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) < 2.5 x ULN.

          -  Absolute neutrophil count (ANC) >= 1 x 10(9)/L.

          -  Platelets >= 100 x 10(9)/L.

          -  Serum creatinine < 1.5 mg/dL or creatinine clearance greater or equal than 60 cc/min
             as defined by the Cockcroft-Gault equation.

          -  Women of childbearing potential should be advised to avoid becoming pregnant while on
             therapy with ruxolitinib and for 30 days after the last dose and practice effective
             methods of contraception. Men should be advised not to father a child while receiving
             treatment with Ruxolitinib and for 30 days after the last dose. Effective methods of
             contraception for this study include barrier methods (e.g., condoms, diaphragm);
             spermicidal jelly or foam; oral, depo provera, or injectable hormonal contraceptives;
             intrauterine devices; tubal ligation; and abstinence.

        Exclusion Criteria:

          -  For the phase I portion of the study, patients in blast phase. For the phase II
             portion of the study, patients in accelerated or blast phase.

          -  Patients receiving any other investigational agents.

          -  Patients who are pregnant or breast-feeding.

          -  Patients with clinically significant heart disease (New York Heart Association [NYHA]
             class III or IV).

          -  Patients with corrected QT (QTc) > 480 msec.

          -  Patients taking a potent CYP3A4 inhibitor that cannot be changed to an alternate drug.

          -  Known or suspected hypersensitivity to ruxolitinib.

          -  Patients with advanced malignant hepatic tumors.

          -  Patients with known active hepatitis B or C, or human immunodeficiency virus (HIV)
             infection.

          -  Patients with other medical conditions or concomitant medications that in the opinion
             of the principal investigator may interfere with the therapeutic treatment.