Chronic lymphocytic leukemia (CLL) is the most common leukemia (cancer of blood cells). The purpose of this study is to assess retreatment with venetoclax-obinutuzumab (VenG) in participants previously treated with fixed duration first-line (IL) therapy of venetoclax in combination with an anti-CD20 antibody +/- X (where X is any additional drug). Adverse events and change in disease activity will be assessed. Venetoclax is an approved drug for the treatment of CLL. Study doctors put the participants in 1 of 2 groups, called cohorts, based on when symptoms of CLL came back after previous treatment in first-line. Approximately 75 adult participants with CLL who have been treated with venetoclax in combination with an anti-CD20 antibody +/- X will be enrolled in the study in approximately 60 sites worldwide. Participants will receive intravenous (IV) obinutuzumab + oral venetoclax (VenG) in 28-day cycles for a total of 6 cycles per cohort, followed by 6 to 18 cycles of venetoclax alone, for a total treatment of 12 to 24 cycles, depending on the cohort. There may be higher treatment burden for participants in this trial compared to their standard of care. Participants will attend regular visits during the study at a hospital or clinic. The effect of the treatment will be checked by medical assessments, blood tests, checking for side effects and completing questionnaires.