• Written informed consent. Participant or legally authorized representative (LAR) must provide written informed consent prior to any study-specific procedures or interventions

• Age \>= 18 years. All genders, races, and ethnic groups will be included

• Ability to swallow and retain oral medication

• Documented previously untreated CLL/SLL. Diagnosis must be confirmed by peripheral blood flow cytometry or lymph node biopsy and made in accordance with international workshop (iw)CLL diagnostic criteria

• Baseline detectable immunoglobulin heavy (IGH) gene signature determined as part of clonoSEQ for minimal residual disease (MRD) testing

• Must meet at least 1 criterion for treatment based on iwCLL guidelines

‣ Evidence of progressive marrow failure as manifested by the onset or worsening of anemia and/or thrombocytopenia, or

⁃ Massive (i.e., lower edge of spleen \>= 6 cm below the left costal margin), progressive, or symptomatic splenomegaly, or

⁃ Massive (i.e., \>= 10 cm in the longest diameter), progressive, or symptomatic lymphadenopathy, or

⁃ Progressive lymphocytosis in the absence of infection, with an increase in blood absolute lymphocyte count (ALC) \> 50% over a 2 month period, or lymphocyte doubling time of \< 6 months (as long as initial ALC was \>= 30,000/uL), or

⁃ Autoimmune anemia and / or thrombocytopenia that is poorly responsive to corticosteroids or other standard therapy, or

⁃ Constitutional symptoms, defined as any one or more of the following disease related symptoms or signs occurring in the absence of evidence of infection:

• Unintentional weight loss of \>= 10% within the previous 6 months, or

∙ Significant fatigue (grade \>= 2), or

∙ Fevers \> 100.5°F or 38.0°C for \>= 2 weeks, or

∙ Night sweats for \> 1 month

⁃ FOR PARTICIPANTS WITH SLL ONLY:

• Presence of measurable lymphadenopathy, defined as the presence of ≥ 1 nodal lesion that measures ≥ 2.0 cm in the longest diameter (LD) and ≥ 1.0 cm in the longest perpendicular diameter (LPD) as assessed by computed tomography (CT) or magnetic resonance imaging (MRI)

‣ Eastern Cooperative Oncology Group (ECOG) performance status =\< 2

⁃ Life expectancy of greater than 12 months, as estimated by the treating physician or investigator

⁃ Absolute neutrophil count (ANC) \> 1,000/mm\^3 (uL)

⁃ Platelet count \> 50,000/mm\^3 (uL).

⁃ Serum creatinine =\< 2 x upper limit of normal (ULN) or creatinine clearance (CrCl) \>= 40 mL/min by Cockcroft-Gault

⁃ Aspartate aminotransferase (AST) =\< 3 x ULN

⁃ Alanine aminotransferase (ALT) =\< 3 x ULN

⁃ Alkaline phosphatase (ALP) =\< 3 x ULN

⁃ Total bilirubin =\< 2.5 x ULN unless documented history of Gilbert's syndrome

⁃ Negative for hepatitis C infection and chronic hepatitis B infection

• Participants with positive serology for hepatitis C virus (HCV) must have been tested for HCV ribonucleic acid (RNA) and are eligible only in the case of negative HCV RNA by polymerase chain reaction (PCR) testing

• Participants must be hepatitis B virus (HBV) negative by serology. Participants with occult or prior HBV infection (defined as negative hepatitis B \[HB\] surface antigen \[sAg\] and positive serology testing for anti-HBV core antigen \[cAb\]) may be included if HBV deoxyribonucleic acid (DNA) was undetectable by PCR, provided that they are willing to undergo monthly ongoing DNA testing. Antiviral prophylaxis may be administered as per institutional guidelines

• Participants who have protective HBV titers of HB surface antibody (sAb) (HBsAb positive, HBcAb negative, and HBsAg negative) after vaccination or previously cured hepatitis B are eligible

‣ Individuals with childbearing potential must have documented negative pregnancy test within the 7 days before the start of any treatment drug and must commit to the use of study approved methods of contraception during study treatment and for 6 months after the last dose of obinutuzumab

⁃ Individuals that can contribute sperm for the conception of a child must commit to the use of study approved methods of contraception during the trial period and for 6 months after the last dose of obinutuzumab. Such individuals must also refrain from donation of sperm during study treatment and for 6 months after the last dose of obinutuzumab

⁃ Individuals of reproductive and lactating potential must agree to stop breastfeeding and refrain from donation of ova from the start of study treatment (cycle \[C\]1 day \[D\]1) and for 6 months after the last dose of obinutuzumab