Inclusion Criteria:  Confirmed diagnosis of CLL/SLL requiring therapy per iwCLL 2018 criteria Previous treatment with at least one line of therapy that may include a covalent Bruton's tyrosine kinase (BTK) inhibitor Platelets greater than or equal to (≥)50 x 10⁹/liter (L), hemoglobin ≥8 grams/deciliter (g/dL) and absolute neutrophil count ≥1.0 x 10⁹/L Adequate organ function Eastern Cooperative Oncology Group (ECOG) Performance Status 0-2 Estimated creatinine clearance ≥30 milliliters per minute (mL/min)  Exclusion Criteria:  Known or suspected Richter's transformation at any time preceding enrollment Prior therapy with a non-covalent (reversible) BTK inhibitor Patients requiring therapeutic anticoagulation with warfarin or another Vitamin K antagonist Current treatment with strong cytochrome P450 (CYP) 3A4 (CYP3A4) inhibitors or inducers and/or strong P-glycoprotein (P-gp) inhibitors Prior therapy with venetoclax Central nervous system (CNS) involvement Active uncontrolled systemic bacterial, viral, fungal, or parasitic infection Known human immunodeficiency virus (HIV) infection, regardless of cluster of differentiation 4 (CD4) count Allogeneic stem cell transplantation (SCT) or chimeric antigen receptor (CAR)-T within 60 days Active hepatitis B or hepatitis C Known active cytomegalovirus (CMV) infection Uncontrolled immune thrombocytopenic purpura (ITP) or autoimmune hemolytic anemia (AIHA) Significant cardiovascular disease Vaccination with a live vaccine within 28 days prior to randomization  Patients with the following hypersensitivity:  Known hypersensitivity to any component or excipient of pirtobrutinib and venetoclax Prior significant hypersensitivity to rituximab Known allergy to allopurinol and inability to take uric acid lowering agent