A Phase 1B Dose Escalation Study to Investigate the Safety, Tolerability and Preliminary Efficacy for the Combination Dasatinib (BMS-354825) Plus Nivolumab (BMS-936558) in Patients Chronic Myeloid Leukemia (CML)

Incidence of Adverse Events (AEs)

Time Frame: Initiation of study drug to discontinuation of nivolumab stop date + 100 days or discontinuation of dasatinib + 30 days

Any new untoward medical occurrence or worsening of a preexisting medical condition in a clinical investigation subject administered an investigational (medicinal) product and that does not necessarily have a causal relationship with this treatment. An AE can therefore be any unfavorable and unintended sign (such as an abnormal laboratory finding), symptom, or disease temporally associated with the use of investigational product, whether or not considered related to the investigational product.

Incidence of Serious Adverse Events (SAEs)

Time Frame: Initiation of study drug to within 100 days of discontinuation of nivolumab dosing and 30 days of dasatinib dosing

Any untoward medical occurrence that at any dose: results in death, is life threatening, requires in persistent or significant disability/incapacity, is a congenital anomaly/birth defect or is a important medical event.Requires inpatient hospitalization or causes prolongation of existing hospitalization, results.

Incidence of Change From Baseline in Clinical Laboratory Tests: Hematology

Time Frame: Up to 40 Months

The number of participants with a shift in laboratory test results from baseline to Grade 3-4 in hematology

Incidence of Abnormalities in Clinical Laboratory Tests: Liver Tests

Time Frame: Up to 40 Months

The number of participants with an abnormal Liver function test. Aspartate aminotransferase (AST) Alanine aminotransferase (ALT) Upper Limit of Normal (ULN)

Incidence of Laboratory Abnormalities in Specific Thyroid Tests

Time Frame: Up to 40 Months

Free T3 (FT3) Free T4 (FT4) Lower Limit of Normal (LLN)

Incidence of Dose Limiting Toxicities (DLT)

Time Frame: Week 3 to week 6

DLT will be determined based on the incidence and intensity of drug related adverse events (AEs). The following drug-related AEs (whether related to one or both agents) occurring during the first 6 weeks of combined treatment with both dasatinib plus nivolumab (ie, Weeks 3 to 8, inclusive) would be considered DLTs: * Grade 4 hematologic AE lasting \> 7 days despite appropriate medical intervention, except as noted below; * Grade 3 or Grade 4 nonhematologic AE irrespective of duration; * Grade 2 nonhematologic AE lasting \> 7 days despite appropriate medical intervention (exception: asymptomatic laboratory values of Grade 2 which do not require medical intervention); * Any toxicity managed by discontinuation of nivolumab; * Grade ≥ 2 AE not controlled by medical intervention and requiring dasatinib treatment interruption for \> 28 consecutive days; * Grade ≥ 2 AE not controlled by medical intervention and requiring missing 2 consecutive doses of nivolumab.