Common Inclusion Criteria:

          1. Patient aged 18y or more

          2. Signed informed consent

          3. Patient with Philadelphia chromosome positive chronic phase CML and M BCR-ABL1
             transcript positivity at diagnosis

          4. Treatment with imatinib, nilotinib, dasatinib or bosutinib for more than 2 years
             overall

          5. No switch between tyrosine kinase inhibitors within the last 3 months

          6. No dose modification within the last 3 months

          7. Complete cytogenetic response or BCR-ABL1IS ≤ 1%

          8. Detectable BCR-ABL1 with BCR-ABL1IS > 0.0032% (less than MR4.5)

          9. ECOG grade 0 to 2

         10. ASAT and ALAT ≤ 2.5 N

         11. Bilirubin in serum ≤ 2.5 N

         12. Men and Women of childbearing potential must be using an adequate method of
             contraception

        These specific inclusion criteria will apply for the Avelumab arm in addition to the common
        criteria.

          1. Hematologic:

               1. Absolute neutrophil count (ANC) ≥ 1.5 × 109/L,

               2. Platelet count ≥ 100 × 109/L,

               3. Hemoglobin ≥ 9 g/dL. (may have been transfused).

          2. Hepatic:

             a. Total bilirubin level ≤ 1.5 × the upper limit of normal (ULN) range.

          3. Renal: Estimated creatinine clearance ≥ 30 mL/min according to the Cockcroft-Gault
             formula (or local institutional standard method)

          4. Pregnancy test: Negative serum or urine pregnancy test at screening for women of
             childbearing potential.

          5. Contraception: Highly effective contraception for both male and female subjects
             throughout the study and for at least 30 days after last Avelumab treatment
             administration if the risk of conception exists.

        Common Exclusion Criteria:

          1. Pregnant or lactating women,

          2. Participation in another clinical trial with any investigative drug within 30 days
             prior to study enrolment,

          3. Prior history of hematopoietic stem cell transplantation (autologous or allogenic)

          4. Cardiovascular disease:

               -  Stage II to IV congestive heart failure (CHF) as determined by the New York Heart
                  Association (NYHA) classification system for heart failure.

               -  Myocardial infarction within the previous 6 months

               -  Symptomatic cardiac arrhythmia requiring treatment

          5. Grade III or IV fluid retention

          6. Known BCR-ABL kinase domain mutation

          7. CML patient not in chronic phase at diagnosis

          8. Individuals with an active malignancy

          9. Known HIV-positivity

        These specific exclusion criteria will apply for the pioglitazone arm in addition to the
        common criteria.

          1. Known osteoporosis with curative therapy (prophylactic therapy is not an exclusion
             criteria)

          2. Patient requiring anti-diabetic medication

        These specific exclusion criteria will apply for the Avelumab arm in addition to the common
        criteria:

          1. IMMUNOSUPRESSANTS: Current use of immunosuppressive medication, EXCEPT for the
             following:

               1. intranasal, inhaled, topical steroids, or local steroid injection (e.g.,
                  intra-articular injection);

               2. Systemic corticosteroids at physiologic doses ≤ 10 mg/day of prednisone or
                  equivalent;

               3. Steroids as premedication for hypersensitivity reactions (e.g., CT scan
                  premedication).

          2. AUTOIMMUNE DISEASE: Active autoimmune disease that might deteriorate when receiving an
             immuno-stimulatory agent. Patients with diabetes type I, vitiligo, psoriasis, or hypo-
             or hyperthyroid diseases not requiring immunosuppressive treatment are eligible.

          3. ORGAN TRANSPLANTATION: Prior organ transplantation including allogenic stem-cell
             transplantation.

          4. INFECTIONS: Active infection requiring systemic therapy.

          5. HIV/AIDS: Known history of testing positive for HIV or known acquired immunodeficiency
             syndrome.

          6. HEPATITIS: Hepatitis B virus (HBV) or hepatitis C virus (HCV) infection at screening
             (positive HBV surface antigen or HCV RNA if anti-HCV antibody screening test positive)

          7. VACCINATION: Vaccination within 4 weeks of the first dose of Avelumab and while on
             trials is prohibited except for administration of inactivated vaccines

          8. HYPERSENSITIIVTY TO STUDY DRUG: Known prior severe hypersensitivity to investigational
             product or any component in its formulations, including known severe hypersensitivity
             reactions tomonoclonal antibodies (NCI CTCAE v4.03 Grade ≥ 3)

          9. CARDIOVASCULAR DISEASE: Clinically significant (i.e., active) cardiovascular disease:
             cerebral vascular accident/stroke (< 6 months prior to enrolment), myocardial
             infarction (< 6 months prior to enrolment), unstable angina, congestive heart failure
             (≥ New York Heart Association Classification Class II), or serious cardiac arrhythmia
             equiring medication.

         10. OTHER PERSISTING TOXICITIES: Persisting toxicity related to prior therapy (NCI CTCAE
             v. 4.03 Grade > 1); however, alopecia, sensory neuropathy Grade ≤ 2, or other Grade ≤
             2 not constituting a safety risk based on investigator's judgment are acceptable.

         11. Other severe acute or chronic medical conditions including immune colitis,
             inflammatory bowel disease, immune pneumonitis, pulmonary fibrosis or psychiatric
             conditions including recent (within the past year) or active suicidal ideation or
             behaviour; or laboratory abnormalities that may increase the risk associated with
             study participation or study treatment administration or may interfere with the
             interpretation of study results and, in the judgment of the investigator, would make
             the patient inappropriate for entry into this study.