Inclusion Criteria:  Age ≥18 years old. Willing and able to give informed consent. Diagnosed with CML in chronic phase and have either the b3a2 (e14a2) or b2a2 (e13a2) variants that give rise to the p210 BCR-ABL protein. Subtype classification whether b3a2 (e14a2) or b2a2 (e13a2) is not required for study eligibility. Must have a documented history of attempting only one prior imatinib discontinuation under the guidance of a treating physician.  Must have met all the following criteria prior to first attempt to discontinue their imatinib:  Stable molecular response (MR4; < 0.01% IS) for > 2 years, as documented on at least four tests, performed at least three months apart (e.g. If a patient has had >4 PCR tests performed during the two years leading up to their initial TKI discontinuation, any value between 0.01 and 0.05% IS is considered a stable result, however, at least four tests must be < 0.01% IS). Treatment with imatinib for a minimum of three years prior to discontinuing imatinib. Must have relapsed (defined as loss of major molecular response (MMR), real-time quantitative polymerase chain reaction (RQ-PCR) for BCR-ABL >0.1% IS after first attempted imatinib discontinuation. After first failed TFR attempt, must have a minimum duration of one year of retreatment with imatinib (up to 400mg PO QD), and must plan to remain on imatinib for a minimum of 12 months during the combination treatment phase. Eastern Cooperative Oncology Group (ECOG) performance status 0-3. Must have a RQ-PCR for BCR-ABL < 0.0032% IS (MR4.5) reported by the trial designated central lab at the time of study enrollment.  Female patients must meet one of the following:  Postmenopausal for at least one year before the screening visit, Surgically sterile, If they are of childbearing potential, agree to practice two effective methods of contraception from the time of signing of the informed consent form through 90 days after the last dose of study drug, Must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence [e.g., calendar, ovulation, symptothermal, postovulation methods] and withdrawal are not acceptable contraception methods.)  Male patients, even if surgically sterilized (i.e., status post vasectomy), must agree to one of the following:  Practice effective barrier contraception during the entire study treatment period and through 90 days after the last study drug dose, Must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence [e.g., calendar, ovulation, symptothermal, postovulation methods] and withdrawal are not acceptable methods of contraception.)  Exclusion Criteria:  A potential subject who meets any of the following exclusion criteria is ineligible to participate in the study.  History of accelerated or blast phase CML. A second malignancy requiring active treatment. History of recent (within 12 months) acute pancreatitis or chronic pancreatitis Subjects who have previously received treatment with asciminib. Subjects with platelet (PLT) count < 100 × 109/L or an absolute neutrophil count (ANC) of < 1 × 109/L or hemoglobin < 8 g/dL. Aspartate aminotransferase (AST) and alanine transaminase (ALT) ≥3 times the institutional upper limit of normal. Creatinine ≥ 2 times the institutional upper limit of normal. Total bilirubin ≥ 1.5 times the institutional upper limit of normal (unless direct bilirubin is within normal limits). Lipase > institutional upper limit of normal. Pregnant or lactating. Unable to comply with lab appointment schedule and patient-reported outcome (PRO) assessments. Another investigational drug within four weeks of enrollment. Any serious medical or psychiatric illness that could, in the investigator's opinion, interfere with the completion of treatment according to this protocol. Patient has undergone a prior allogeneic stem cell transplant. Screening 12-lead ECG showing a baseline corrected QT interval >480msec (patients with a pacemaker will still be eligible with QTc>500msec).