Inclusion Criteria:

          -  Male or female patients with diagnosis of CP-CML with cytogenetic confirmation of the
             Ph+ chromosome [t(9;22)(q34;q11)].

          -  Ph-negative cases or patients with variant translocations who are BCR-ABL1 positive in
             multiplex PCR 35 will be also considered eligible.

          -  ECOG performance status of ≤2.

          -  Age ≥ 18 years old (no upper age limit is given)

          -  Serum levels of potassium, magnesium, total calcium within the normal limits (≥LLN
             [lower limit of normal] and ≤ULN [upper limit of normal]). Correction of electrolytes
             levels with supplements to fulfil enrolment criteria is allowed.

          -  AST and ALT ≤2.5 x ULN or 5.0 x ULN if considered due to leukemia

          -  Alkaline phosphatase ≤2.5 x ULN unless considered due to leukemia

          -  Total bilirubin ≤1.5 x ULN, except known Gilbert disease

          -  Serum creatinine ≤2 x ULN

          -  Written informed consent prior to any study procedures being performed.

        Exclusion Criteria:

          -  Allogeneic stem cell transplantation

          -  Known impaired cardiac function, including any of the following:

               -  Congenital long QT syndrome

               -  History of or presence of clinically significant ventricular or atrial
                  tachyarrhythmia

               -  QTc >450 msec on screening ECG

               -  Myocardial infarction within 12 months prior to starting therapy

          -  Other clinical significant heart disease (e.g. unstable angina, congestive heart
             failure)

          -  Acute or chronic viral hepatitis with moderate or severe hepatic impairment
             (Child-Pugh scores >6), even if controlled

          -  Other concurrent uncontrolled medical conditions (e.g., active or uncontrolled
             infections, acute or chronic liver and renal disease) that could cause unacceptable
             safety risks or compromise compliance with the protocol

          -  Impaired gastrointestinal function or disease that may alter the absorption of study
             drug (e.g., ulcerative disease, uncontrolled nausea, vomiting and diarrhea,
             malabsorption syndrome, small bowel resection or gastric by-pass surgery)

          -  Concomitant medications known to be strong inducers or inhibitors of the CYP450
             isoenzyme CYP3A4

          -  Patients who have undergone major surgery ≤2 weeks prior to starting study drug or who
             have not recovered from side effects of such therapy

          -  Patients who are pregnant or breastfeeding or women of reproductive potential not
             employing an effective method of birth control. Women of childbearing potential must
             have a negative serum pregnancy test within 14 days of study start. Post-menopausal
             women must be amenorrheic for at least 12 months in order to be considered of
             non-childbearing potential. Male and female patients must agree to employ an effective
             method of birth control throughout the study and for up to 2 weeks following
             discontinuation of study drug

          -  Known diagnosis of human immunodeficiency virus (HIV) infection (HIV testing is not
             mandatory)

          -  Known serious hypersensitivity reactions to asciminib, imatinib, nilotinib or
             dasatinib

          -  Patients with a history of another primary malignancy that is currently clinically
             significant or currently requires active intervention

          -  Patients unwilling or unable to comply with the protocol.