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.