Inclusion Criteria:

          -  Diagnosis CLL/small lymphocytic lymphoma (SLL) and be untreated

          -  Patients must have an indication for treatment by 2018 International Workshop on
             Chronic Lymphocytic Leukemia (IWCLL) Criteria

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0-2

          -  Patients of childbearing potential must be willing to practice highly effective birth
             control during treatment and for 2 days after the last dose of acalabrutinib or 18
             months after the last dose of obinutuzumab, whichever is later

          -  A negative urine pregnancy test (within 7 days of day 1) is required for women with
             childbearing potential

          -  Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) except for patients
             with bilirubin elevation due to Gilbert's disease who will be allowed to participate

          -  An alanine transferase (ALT) =< 2.5 x ULN

          -  An estimated creatinine clearance (CrCl) of > 30 mL/min, as calculated by the
             Cockcroft-Gault equation unless disease related

          -  Free of prior malignancies for 2 years with exception of patients diagnosed with basal
             cell or squamous cell carcinoma of the skin, or carcinoma "in situ" of the cervix or
             breast who are eligible even if they are currently treated or have been treated and/or
             diagnosed in the past 2 years prior to study enrollment. If patients had another
             malignancy of indolent behavior in the past 2 years prior to study enrollment that is
             expected to be cured with treatment they received such patients can be enrolled, after
             consultation with the principal investigator

        Exclusion Criteria:

          -  Pregnant or breast-feeding females

          -  Prior CLL/SLL treatment

          -  Known history of infection with human immunodeficiency virus (HIV) or any uncontrolled
             active significant infection (eg, bacterial, viral or fungal)

          -  Signs of active hepatitis B or C. Subjects who are hepatitis B core antibody
             (anti-HBc) positive and who are surface antigen negative will need to have a negative
             polymerase chain reaction (PCR). Those who are hepatitis B surface antigen (HBsAg)
             positive or hepatitis B PCR positive will be excluded. Subjects who are hepatitis C
             antibody positive will need to have a negative PCR result. Those who are hepatitis C
             PCR positive will be excluded

          -  Patients with uncontrolled autoimmune hemolytic anemia (AIHA) or autoimmune
             thrombocytopenia (ITP)

          -  An absolute neutrophil count of less than 500/uL, unless disease-related at time of
             screening for this protocol

          -  A platelet count of less than 30,000/uL at time of screening for this protocol

          -  Clinically significant cardiovascular disease such as uncontrolled or symptomatic
             arrhythmias, congestive heart failure, or myocardial infarction within 6 months of
             heart failure, or any class 3 or 4 cardiac disease as defined by the New York Heart
             Association Functional Classification. Subjects with controlled, asymptomatic atrial
             fibrillation can enroll. Patients with a history of paroxysmal atrial fibrillation
             (PAF) or deep vein thrombosis or pulmonary embolism (DVT/PE) can be included if they
             had no signs of PAF or DVT/PE in the last 6 months before enrolment. Patients with
             ongoing atrial fibrillation (AFib) or ongoing PAF or DVT/PE should be excluded

          -  History of stroke or cerebral hemorrhage within 6 months

          -  Known history or evidence of bleeding diathesis or coagulopathy within 3 months

          -  Major surgical procedure, open biopsy, or significant traumatic injury within 28 days

          -  Minor surgical procedures, fine needle aspirations or core biopsies within 7 days
             prior to day 1. Bone marrow aspiration and/or biopsy are allowed

          -  Serious, non-healing wound, ulcer, or bone fracture

          -  Treatment with warfarin (Coumadin) or any other vitamin K antagonist. Patients who
             recently received warfarin must be off warfarin for at least 7 days prior to start of
             the study. Patients receiving novel oral anticoagulant (NOAC), also termed direct oral
             anticoagulant (DOAC) are permitted to enroll. Patients who are currently on a vitamin
             K antagonist must be switched to a non-vitamin K antagonist, such as a NOAC/DOAC

          -  Has difficulty with or is unable to swallow oral medication, or has significant
             gastrointestinal disease that would limit absorption of oral medication

          -  Known history of drug-specific hypersensitivity or anaphylaxis to study drug
             (including active product or excipient components)

          -  Requires treatment with a strong cytochrome P450 3A4 (CYP3A4) inhibitor/inducer

          -  Prothrombin time (PT)/international normalized ratio (INR) or activated partial
             thromboplastin time (aPTT) (in the absence of lupus anticoagulant) > 2 x ULN

          -  Requires treatment with proton pump inhibitors

          -  Concurrent participation in another therapeutic clinical trial