Asciminib Used in Consolidation With Imatinib vs. Imatinib to Achieve TFR in CP-CML

Inclusion Criteria: In order to be eligible, candidates must fulfill all the following criteria: 1. Male or female patients aged at least 18 years of age with a confirmed diagnosis of CML-CP. 2. Written informed consent prior to any screening procedures 3. Available and willing to comply with all study assessments. 4. Imatinib treatment ongoing \> 4 years, and currently receiving: * Standard dose 400 mg PO QD or; * 300 mg PO QD for at least 6 months (see below) 5. CML in deep molecular response (DMR, at least MR4 IS) for at least 12 months prior to randomization (documented through at least 3 PCRs test results over the period of 12 months prior to randomization, showing BCR-ABL1 levels ≤ 0.01% IS (International Scale) and no result over \>0.01%). For patients receiving 300 mg imatinib QD, minimum of two (2) of those qPCRs evaluations must have been obtained at least 3 months apart while on 300 mg imatinib. 6. ECOG performance status of 0-2. 7. Adequate organ function, defined by: * Absolute Neutrophil Count (ANC) ≥ 1.5 x 10\^9/L * Platelets ≥ 75 x 10\^9/L (without the requirement for transfusion for 14 days) * Hemoglobin ≥ 90 g/L (without the requirement for transfusion for 14 days) * Serum creatinine \< 132 µmol/L * Total bilirubin ≤ 1.5 x ULN (except for patients with Gilbert's syndrome who may only be included with total bilirubin ≤ 3.0 x ULN) * Aspartate transaminase (AST) ≤ 3.0 x ULN * Alanine transaminase (ALT) ≤ 3.0 x ULN * Alkaline phosphatase ≤ 2.5 x ULN * Serum lipase ≤ 1.5 x ULN 8. Serum levels of potassium, magnesium, total calcium within the normal laboratory range. Correction of electrolytes levels with supplements to fulfil enrolment criteria is allowed. * potassium increase of up to 6.0 mmol/L is acceptable if associated with creatinine clearance within normal limits (as estimated by the Cockcroft-Gault formula, appendix 1) * calcium increase to 3.1 mmol/L is acceptable if associated with creatinine clearance within normal limits * magnesium increase up to 1.23 mmol/L if associated with creatinine clearance within normal limits 9. No previous CML-AP/BP by MDACC criteria nor resistance to TKI by ELN criteria. 10. Never attempted TFR 11. Women of child-bearing potential (WOCBP), defined as all women physiologically capable of becoming pregnant, must have a negative serum pregnancy test before initiation of study treatment, and must also use highly effective methods of contraception to continue for at least 14 days after the last dose of study treatment, or for the duration of a monthly cycle of oral contraception, whichever is longer. Acceptable forms of highly effective contraception methods include: 1. Total abstinence (when this is in line with the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception 2. Male/female sterilization defined as: 1. Female sterilization (have had surgical bilateral oophorectomy with or without hysterectomy) or tubal ligation at least six weeks before taking study treatment. In case of oophorectomy alone, only when the reproductive status of the woman has been confirmed and documented by follow up hormone level assessment 2. Male sterilization of the sole partner (at least 6 months prior to screening) of a female patient on the study. 3. A combination of any two of the following (i+ii or i+iii or ii+iii): i) Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/ vaginal suppository ii) Use of oral, injected or implanted hormonal methods of contraception or other forms of hormonal contraception that have comparable efficacy (failure rate \<1%), for example hormone vaginal ring or transdermal hormone contraception iii) Placement of an intrauterine device (IUD) or intrauterine system (IUS) Exclusion Criteria: 1. Patients known to be in second CP-CML after previous progression to AP/BC-CML 2. Previous treatment with a TKI other than imatinib. 3. Prior allogeneic transplant. 4. Tolerance concerns to continue imatinib on study, as determined by the investigator. 5. Treatment with strong inducers/inhibitors of CYP3A4. 6. Known atypical ABL1-BCR transcript that precludes use of IS system for monitoring. 7. Current or prior history of another malignancy within the past 2 years, unless it is a solid tumor with a life expectancy of at least 3 years and its treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen (for example, patients who have undergone complete resection of an in situ carcinoma, or who have a low risk indolent prostate cancer are eligible). History or current diagnosis of cardiac disease indicating significant risk or safety for subjects participating in the study such as: 1. History of myocardial infarction, angina pectoris, coronary artery bypass graft within 6 months prior to randomization 2. Concomitant clinically significant arrhythmias 3. Resting QTcF ≥ 450 msec (male) or ≥ 460 msec (female) prior to randomization 4. Long QT syndrome, family history of idiopathic sudden death or congenital long QT syndrome, or any of the following: i. Risk factors for Torsades de Pointes ii. Concomitant medications with a "known" risk of Torsades de Pointes iii. inability to accurately determine the QTcF interval, unless this is due to the presence of a pacemaker. 8. History of acute pancreatitis within 1 year prior to randomization or medical history of chronic pancreatitis; on-going acute liver disease or history of chronic liver disease 9. Patients who have undergone major surgery ≤2 weeks prior to starting study drug or who have not recovered from side effects of such therapy 10. Subjects with other severe or uncontrolled medical conditions that in the opinion of the investigator may compromise their compliance with the protocol or may represent an unacceptable risk to their safety (e.g. uncontrolled diabetes, active or uncontrolled infection, uncontrolled clinically significant hyperlipidemia and high serum amylase). 11. Treatment with other investigational agents (defined as not used in accordance with the approved indication) within 4 weeks of Day 1. 12. Known allergy or hypersensitivity to asciminib or any of its excipients. 13. Patients who are pregnant or breastfeeding or WOCBP not employing an effective method of birth control. 14. Known infection with Human Immunodeficiency virus (HIV), chronic Hepatitis B (HBV) or chronic hepatitis C infection (HCV). Hepatitis B and C testing will be performed at screening.