Inclusion Criteria:

          -  Patients must have a diagnosis of chronic phase chronic myeloid leukemia without any
             history of progression to accelerated or blast phase CML; no new bone marrow
             aspiration and biopsy is needed to prove diagnosis prior to randomization; however,
             documentation stating the patient is in chronic phase is required

          -  Patients must have detectable BCR-ABL transcripts measured by reverse transcriptase
             (RT)-PCR at a clinical laboratory improvement act (CLIA)-approved laboratory and
             reported on the international scale (IS) with a value of > 0.0032% IS and =< 1.0% IS
             within 21 days prior to randomization; the RT-PCR assay must have the sensitivity to
             detect a 4.5 log reduction in BCR-ABL transcripts from 100% IS (0.0032% IS or lower)

          -  Patients must have been receiving TKI treatment for CML for at least 12 months prior
             to randomization

          -  Patients must be currently receiving treatment with bosutinib (within the allowable
             dose range of 200-500 mg daily), nilotinib (within the allowable dose range of 150-400
             mg BID or a cumulative daily dose of 300-800 mg), or dasatinib (within the allowable
             dose range of 40-140 mg daily); they must have received their current TKI for a
             minimum of 6 months prior to randomization and must be expected to remain on the same
             TKI for the next 12 months

          -  Patient must not have a history of resistance to any prior TKI drug; if patient has
             received more than one TKI, the reason for changing treatment must have been
             intolerance to the prior TKI and the treatment change must have occurred >= 6 months
             prior to randomization

          -  Patients must not be receiving any other investigational agents

          -  Patients must have complete history and physical examination within 28 days prior to
             randomization

          -  If clinically indicated, patients must have corrected Fridericia's correction formula
             (QTcF) interval < 500 ms (by Fridericia calculation) on a 12-lead electrocardiography
             (EKG) within 7 days prior to randomization

          -  Platelets >= 100,000/mm^3 (100.0 x 10^9/L) within 7 days prior to randomization

          -  Absolute neutrophil count (ANC) > 1,000/mm^3 (1.0 x 10^9/L) within 7 days prior to
             randomization

          -  Hemoglobin >= 8 g/dL within 7 days prior to randomization

          -  Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =< 2.5 x
             institutional upper limit of normal (IULN) within 7 days prior to randomization

          -  Total bilirubin =< 1.5 x IULN within 7 days prior to randomization (unless the patient
             has a known diagnosis of Gilbert's syndrome)

          -  Serum creatinine =< 1.5 x IULN within 7 days prior to randomization

          -  Prior malignancy is allowed providing it does not require concurrent therapy;
             exception: active hormonal therapy is allowed

          -  Patients must not be pregnant or nursing due to the teratogenic potential of the drugs
             used on this study; women of child-bearing potential must have a negative serum
             pregnancy test within 7 days prior to randomization; women/men of reproductive
             potential must have agreed to use an effective contraceptive method during treatment
             and for 30 days after discontinuation of study drug; a woman is considered to be of
             "reproductive potential" if she has had menses at any time in the preceding 12
             consecutive months; in addition to routine contraceptive methods, "effective
             contraception" also includes heterosexual celibacy and surgery intended to prevent
             pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy,
             bilateral oophorectomy or bilateral tubal ligation; however, if at any point a
             previously celibate patient chooses to become heterosexually active during the time
             period for use of contraceptive measures outlined in the protocol, he/she is
             responsible for beginning contraceptive measures

          -  Patients known to be human immunodeficiency virus positive (HIV+) are eligible
             provided they meet all other eligibility criteria and have undetectable HIV viral
             loads on their most recent viral load test which must have been performed in the last
             6 months

          -  Specimens (peripheral blood) must be collected and submitted to a CLIA-approved
             laboratory, within 21 days prior to randomization; BCR-ABL transcripts must be
             measured using RT-PCR and results must be reported using the international scale; the
             RT-PCR assay must have the sensitivity to detect a 4.5 log reduction in BCR-ABL
             transcripts from 100% IS (must be able to detect 0.0032% IS or lower)

          -  Patients must be offered participation in submission of specimens for central BCR-ABL
             quantification and banking for future specimens; this submission is highly encouraged
             as an important protocol endpoint; with patient's consent, specimens must be collected
             and submitted, within 21 days prior to randomization

          -  Patients must be informed of the investigational nature of this study and must sign
             and give written informed consent in accordance with institutional and federal
             guidelines

          -  As a part of the Oncology Patient Enrollment Network (OPEN) registration process the
             treating institution's identity is provided in order to ensure that the current
             (within 365 days) date of institutional review board approval for this study has been
             entered in the system