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