Study of Pts With Philadelphia Chromosome-Pos ALL With Comb of Ibrutinib, Dasatinib, and Prednisone

Inclusion Criteria: * Confirmed new diagnosis of Philadelphia chromosome-positive or BCR-ABL1 positive precursor B cell acute lymphoblastic leukemia (B-ALL) based on ≥ 20% lymphoblasts in bone marrow or blood. Outside specimens will be subject to central review at the HCI (Huntsman Cancer Institute) Department of Pathology. BCR-ABL1 or Philadelphia-chromosome positivity may be determined by RT-PCR, conventional cytogenetics and/or FISH. * Men and woman ≥ 50 years of age * ECOG status 0 - 2 * Biochemical values as defined by the protocol. * Women of childbearing potential and men who are sexually active must be practicing a highly effective method of birth control during and after the study consistent with local regulations regarding the use of birth control methods for subjects participating in clinical trials. Men must agree to not donate sperm during and after the study. For women, these restrictions apply for 1 month after the last dose of study drug. For men, these restrictions apply for 3 months after the last dose of study drug. * Women of childbearing potential must have a negative serum (beta-human chorionic gonadotropin \[β-hCG\]) or urine pregnancy test at screening within 7 days of enrollment. * Able to provide informed consent and willing to sign an approved consent form that conforms to federal and institutional guidelines. Exclusion Criteria: * Major surgery or a wound that has not fully healed within 4 weeks of enrollment. * Prior exposure to dasatinib (\>7 days), Bruton's tyrosine kinase inhibitor exposure, or prior chemotherapy for ALL (up to 7 days of steroids are allowed) * History of stroke or intracranial hemorrhage within 6 months prior to enrollment. * Grade ≥ 2 QTc prolongation on screening ECG within 28 days of enrollment, or history of ventricular arrhythmia. * Clinically significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of screening, or any Class 3 (moderate) or Class 4 (severe) cardiac disease as defined by the New York Heart Association Functional Classification. * Hepatic impairment (Child Pugh Classes A- C) that is not considered to be the result of leukemic involvement as determined by the PI * Requires anticoagulation with warfarin or equivalent vitamin K antagonists (eg, phenprocoumon). * Requires chronic treatment with strong CYP3A inhibitors. * Vaccinated with live, attenuated vaccines within 4 weeks of enrollment. * Known history of human immunodeficiency virus (HIV) or active Hepatitis C Virus or active Hepatitis B Virus infection or any uncontrolled active systemic infection. * Women who are pregnant or breastfeeding. * Herbal preparations or over-the-counter supplements containing herbal ingredients (St. John's Wort, Estroven, Blue Cohosh) are prohibited during treatment and must be stopped within 24h of first dose of ibrutinib. * Any life-threatening illness, medical condition, or organ system dysfunction which, in the investigator's opinion, could compromise the subject's safety, interfere with the absorption or metabolism of ibrutinib capsules, or put the study outcomes at undue risk. * Known central nervous system lymphoma (does not include diagnosis of ALL with CNS involvement)