Inclusion Criteria:

          -  Patients with a diagnosis of Philadelphia chromosome (Ph)- or BCR-ABL1-positive CML
             (as determined by cytogenetics, fluorescence in situ hybridization [FISH], or
             polymerase chain reaction [PCR])

          -  Patients should be receiving therapy with nilotinib or dasatinib, whether as initial
             therapy or after prior TKI, at a dose equal or lower than the standard dose

          -  Patients must have received TKI therapy for at least 24 months and not have required
             dose reductions, escalations, discontinuation or re-initiation after discontinuation
             of TKI in the last 6 months

          -  Patients must be in CCyR (by conventional karyotype or FISH, or BCR-ABL/ABL =< 1% IS
             if no cytogenetic analysis available within 3 months)

          -  Patients must have detectable BCR-ABL1 transcript levels meeting at least one of the
             following criteria: a. Patient has never achieved a MMR after 18 months of therapy
             with their current TKI, or b. Patient has not achieved MR4.5 after 36 months of
             therapy with their current TKI, or c. Patient has lost MMR or MR4.5 confirmed in at
             least two consecutive analyses separated by at least 1 month, or d. BCR-ABL1
             transcript levels have reached a plateau defined as a ratio that is stable in a
             molecular response category (i.e., MMR, MR4 or MR4.5) in the last at least 12 months,
             with at least 3 values obtained during this period

          -  Patients must not have had a known continuous interruption of TKI therapy of greater
             than 14 days or for a total of 6 weeks in the 6 months prior to enrollment, unless the
             interruption was for an accident, unrelated hospitalization or surgical procedure, or
             for a treatment-free remission attempt that was unsuccessful and required
             re-initiation of therapy

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

          -  Creatinine =<1.5 x institutional upper limit of normal

          -  Amylase and lipase values =< 3.0 x institutional upper limit of normal

          -  Alkaline phosphatase =< 2.5 x institutional upper limit of normal unless considered to
             be not of hepatic origin

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 3 x institutional upper limit of normal

          -  Total bilirubin =< 1.5 x institutional upper limit of normal (=< 3 x upper limit of
             normal in patients with known Gilbert's syndrome)

          -  The effects of ABL001 on the developing human fetus are unknown. For this reason,
             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. Women of child-bearing potential must agree to
             use highly effective methods of contraception during dosing and for 30 days after
             study treatment. 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. Allowable methods of birth control: Total abstinence (when this
             is in line with the preferred and usual lifestyle of the subject). Periodic abstinence
             (e.g., calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are
             not acceptable methods of contraception. Female sterilization (have had surgical
             bilateral oophorectomy with or without hysterectomy), total hysterectomy, or tubal
             ligation at least six weeks before the start of study treatment. In case of
             oophorectomy alone, only when the reproductive status of the woman has been confirmed
             by follow up hormone level assessment. Male sterilization (at least 6 months prior to
             screening). The vasectomized male partner should be the sole partner for that subject.
             Use of oral, injected or implanted hormonal methods of contraception or placement of
             an intrauterine device (IUD) or intrauterine system (IUS), or other forms of hormonal
             contraception that have comparable efficacy (failure rate <1%), for example hormone
             vaginal ring or transdermal hormone contraception. Sexually active males must use a
             condom during intercourse while taking the drug and for 30 days after stopping
             treatment and should not father a child in this period. A condom is required to be
             used also by vasectomized men in order to prevent delivery of the drug via seminal
             fluid

        Exclusion Criteria:

          -  Patients with New York Heart Association (NYHA) class III or IV congestive heart
             failure or left ventricular ejection fraction (LVEF) < 40% by echocardiogram or
             multigated acquisition (MUGA) scan

          -  Patients with a history of myocardial infarction within the last 6 months or
             unstable/uncontrolled angina pectoris or history of severe and/or uncontrolled
             ventricular arrhythmias. Clinically significant cardiac arrhythmias (e.g., ventricular
             tachycardia), complete left bundle branch block, high-grade atrioventricular (AV)
             block (e.g., bifascicular block, Mobitz type II and third degree AV block)

          -  Corrected QT interval (QTc) of > 480 milliseconds (ms) on baseline electrocardiogram
             (ECG) (using corrected QT interval per institutional standard)

          -  Long QT syndrome, family history of idiopathic sudden death or congenital long QT
             syndrome, or any of the following: a. Risk factors for Torsades de Pointes (TdP)
             including uncorrected hypokalemia or hypomagnesemia, history of cardiac failure, or
             history of clinically significant/symptomatic bradycardia. b. Concomitant
             medication(s) with a known risk to prolong the QT interval and/or known to cause
             Torsades de Pointes that cannot be discontinued or replaced 7 days prior to starting
             study drug by safe alternative medication

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

          -  Patients with known conditions that would significantly affect the ingestion or
             gastrointestinal absorption of drugs administered orally

          -  Nursing women, women of childbearing potential (WOCBP) with positive blood or urine
             pregnancy test, or women of childbearing potential who are not willing to maintain
             adequate contraception

          -  History of acute pancreatitis within 1 year of study entry or past medical history of
             chronic pancreatitis

          -  Absolute neutrophil count (ANC) < 500/mm^3

          -  Platelet count < 50,000 mm^3

          -  History of other active malignancy within 2 years prior to study entry with the
             exception of previous or concomitant basal cell skin cancer and previous carcinoma in
             situ treated curatively

          -  Treatment with medications that meet one of the following criteria and that cannot be
             discontinued at least one week prior to the start of treatment with study treatment:
             Moderate or strong inducers of CYP3A. Moderate or strong inhibitors of CYP3A and/or
             P-glycoprotein (P-gp). Substrates of CYP3A4/5, CYP2C8, or CYP2C9 with narrow
             therapeutic index

          -  Previous treatment with or known/ suspected hypersensitivity to ABL001 or any of its
             excipients

          -  Subject has any other significant medical or psychiatric history that in the opinion
             of the investigator would adversely affect participation in this study