Inclusion Criteria:
* Men and women ≥ 18 years of age with a confirmed diagnosis of CLL, which has relapsed after, or been refractory to, ≥ 1 previous treatments for CLL; however, subjects with 17p deletion are eligible if they have relapsed after, or been refractory to, 1 prior treatment for CLL.
* Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2.
* Agreement to use contraception during the study and for 30 days after the last dose of study drugs if sexually active and able to bear or beget children.
Exclusion Criteria:
* Prior malignancy, except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, or other cancer from which the subject has been disease free for ≥ 2 years or which will not limit survival to \< 2 years.
* A 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 acalabrutinib and/or ACP-319, or put the study outcomes at undue risk.
* Significant cardiovascular disease.
* Malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel or ulcerative colitis, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction.
* Any immunotherapy within 4 weeks of first dose of study drug.
* For subjects with recent chemotherapy or experimental therapy the first dose of study drug must occur after 5 times the half-life of the agent(s).
* History of prior allogeneic bone marrow progenitor cell or solid organ transplantation.
* Ongoing immunosuppressive therapy, including systemic or enteric corticosteroids for treatment of CLL or other conditions. Note: Subjects may be using topical or inhaled corticosteroids as therapy for comorbid conditions.
* Central nervous system (CNS) involvement by CLL.
* Grade ≥ 2 toxicity (other than alopecia).
* Known history of human immunodeficiency virus (HIV) or active infection with hepatitis C virus (HCV) or hepatitis B virus (HBV) or any uncontrolled active systemic infection.
* Uncontrolled autoimmune hemolytic anemia or idiopathic thrombocytopenia purpura.
* Absolute neutrophil count (ANC) \< 0.75 x 109/L or platelet count \< 50 x 109/L unless due to disease involvement in the bone marrow.
* Creatinine \> 1.5 x institutional upper limit of normal (ULN); total bilirubin \> 1.5 x ULN (unless due to Gilbert's disease); and aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \> 2.5 x ULN unless disease related.
* Significant screening ECG abnormalities including left bundle branch block, 2nd degree AV block type II, 3rd degree block, Grade 2 or higher bradycardia, and QTc \> 480 msec.
