Inclusion Criteria:

1. Patients 18 years or older with Philadelphia chromosome (Ph)-positive or
BCR/ABL-positive CML (as determined by cytogenetics, FISH, or PCR).

2. 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.

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

4. 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 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.

5. 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 0.28 in the MDACC molecular diagnostic laboratory), & 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 & lacks a sustained complete molecular response
(CMR, defined as transcript levels still detectable in the MDACC molecular diagnostic
laboratory).

6. 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.

7. 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.

8. ECOG performance status
9. Adequate organ function defined as: bilirubin <2x upper limit of normal (ULN) (unless
associated with Gilbert's syndrome), and ALT or AST <2.5x ULN.

10. ANC >/=1 x10(9)/L and platelets >/=100 x10(9)/L.

11. Serum creatinine < 1.5 mg/dL or creatinine clearance greater or equal than 60 cc/min
as defined by the Cockcroft-Gault Equation: Males(mL/min):(140-age)*IBW(kg) /
72*(serum creatinine (mg/dl)); Females (mL/min):0.85*(140-age)*IBW(kg) / 72*(serum
creatinine (mg/dl)).

12. 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:

1. 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.

2. Patients receiving any other investigational agents.

3. Patients who are pregnant or breast-feeding.

4. Patients with clinically significant heart disease (NYHA Class III or IV).

5. Patients with QTc > 480 msec.

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

7. Known or suspected hypersensitivity to ruxolitinib.

8. Patients with advanced malignant hepatic tumors.

9. Patients with known active hepatitis B or C, or HIV infection.

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