A Randomized Phase II Study Of Bruton Tyrosine Kinase Inhibitor With Or Without Venetoclax In Veterans With Chronic Lymphocytic Leukemia (CLL)/Small Lymphocytic Lymphoma (SLL)

Inclusion Criteria: * CLL or SLL diagnosis * Patients must have been diagnosed with CLL (\> 5000 B-cells per uL of peripheral blood at any point during the course of their disease) or small lymphocytic lymphoma (SLL) with \<5000 B-cells per µL of blood but with disease-associated lymphadenopathy by 2018 IWCLL criteria. * Prior treatment * Patients must be currently receiving CLL/SLL directed therapy with a BTKi (i.e., ibrutinib, acalabrutinib, zanubrutinib) for at least six months. * The dose of BTKi must be stable for at least the past three months. * Age 18 years * ECOG performance status 0-2 * Detectable or measurable CLL/SLL in blood or imaging during the screening period. Detectable CLL/SLL in the blood is defined either by elevation in absolute lymphocyte count or by diagnostic flow cytometry from blood demonstrating presence of CLL cells. * Low TLS risk, defined as having all lymph nodes less than 5 cm in diameter (radiographically) and absolute lymphocyte count less than 25 x 109/L in blood, within 30 days of enrollment. * Required initial laboratory values * Absolute Neutrophil Count (ANC) 1,000/mm3 except if due to bone marrow involvement * Platelet Count (untransfused) 30,000/mm3 except if due to bone marrow involvement * Calc. Creatinine Clearance 40 mL/min (by Cockcroft-Gault) * Bilirubin 1.5 x upper limit of normal (ULN) except if due to liver involvement, hemolysis, or Gilbert's disease * AST / ALT 2.5 x upper limit of normal (ULN) except if due to liver involvement * Other * Patients must be able to swallow oral medications and not have the following conditions: disease significantly affecting gastrointestinal absorption, resection of the stomach or small bowel, partial or complete bowel obstruction. * Patients must be able to receive either a xanthine oxidase inhibitor or rasburicase Exclusion Criteria: * Prior treatment * Patients must not have progression of CLL/SLL on BTKi therapy prior to initiation of the study therapy. * Patients must not have received the combination of BTKi + venetoclax previously. * Comorbid conditions or other active diseases * Patients must not have any history of Richter's transformation or prolymphocytic leukemia. * If evidence of chronic hepatitis B virus (HBV) infection, HBV viral load must be undetectable and be on suppressive therapy, if indicated. * Please note: IVIG can cause a false positive hepatitis B serology. If patients receiving routine IVIG have core antibody or surface antigen positivity without evidence of active viremia (negative hepatitis B DNA) they may still participate in the study, must have hepatitis serologies and hepatitis B DNA monitored periodically by the treating physician. * If history of hepatitis C virus (HCV) infection, must be treated with undetectable HCV viral load. * Patients with Class III or Class IV heart failure by New York Heart Association, those with unstable angina, and those with uncontrolled arrhythmia are not eligible. * Human immunodeficiency virus (HIV)-infected patients on effective antiretroviral therapy are eligible for this trial. * Concomitant medications * Patients must not be receiving active systemic anticoagulation with heparin or warfarin. Patients on warfarin must discontinue the drug for at least 10 days prior to registration on the study. * Chronic concomitant treatment with strong inhibitors of CYP3A4/5 is not recommended on this study. Patients on strong CYP3A inhibitors must discontinue the drug for 14 days prior to registration on the study or discuss with the study principal investigator. * Chronic concomitant treatment with strong CYP3A4/5 inducers is not recommended. Patients must discontinue the drug 14 days prior to registration on the study or discuss with the study principal investigator. * Patients must not require more than 20 mg prednisone or equivalent corticosteroid daily. * Patients must not have uncontrolled active systemic infection requiring intravenous antibiotics