Inclusion Criteria:

- PHASE I: Patients must have chronic phase chronic myeloid leukemia (CML). They must
also be under treatment with nilotinib as either first or second-line therapy.

- PHASE II EXPANSION: Patients must have chronic phase CML and be undergoing treatment
with first-line nilotinib for 6-18 months.

- Patients must have at least a complete cytogenetic response (CCyR) to be eligible for
Phase I. Patients must have a complete cytogenetic response (CCyR) OR must have been
on nilotinib for a minimum of six months in order to be eligible for Phase II of this
study.

- 18 years of age or older and must be able to speak and read English or Spanish

- Must not have undergone treatment for any other form of cancer (aside from
non-melanoma skin cancer) in the past 5 years

- Must be able to provide informed consent

- For the phase I component, prior therapy with a Tyrosine Kinase Inhibitor (TKI) other
than nilotinib is allowable, however, nilotinib must be the current therapy. There
are no restrictions as to how long patients received the alternate therapy, the dose
of alternate therapy, or how long they have been receiving nilotinib, assuming they
have achieved a CCyR. If patients have not achieved a CCyR, they must have been on
nilotinib for a minimum of 6 months. All patients enrolled in this phase must be
under the care of a Moffitt Cancer Center physician, and enrollment for this phase is
expected to be complete within 6 months. The dose of nilotinib for patients receiving
the drug in the second line setting due to failure of a first line TKI is generally
400 mg PO BID. In addition, if a patient is unable to tolerate second line nilotinib
at 400 mg PO BID their dose may be decreased to 300 mg PO BID. In both instances they
will be eligible for phase I.

- For the phase II expansion, patients must not have received any TKI prior to
nilotinib, and must have been under treatment with nilotinib for 6-18 months.
Patients must have a complete cytogenetic response at the time of enrollment.

- Eastern Cooperative Oncology Group (ECOG) performance status ≤2 (Karnofsky ≥60%

- Patients must have normal organ and marrow function as defined below:

- leukocytes ≥3,000/mL

- absolute neutrophil count ≥1,500/mL

- platelets ≥100,000/mL

- total bilirubin within normal institutional limits

- aspartic transaminase/alanine transaminase (AST/ALT) ≤2.5 X institutional upper
limit of normal (ULN)

- creatinine within normal institutional limits - OR -

- creatinine clearance ≥60 mL/min/1.73 m^2 for patients with creatinine levels
above institutional normal

- 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

- Beta human chorionic gonadotrophin (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

- Patients with a 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.

- Patient 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 PO BID are not eligible for phase I however they
will be eligible for phase II.