Phase I Study of JWCAR029 in Subjects With R/R CLL/SLL

Inclusion Criteria: * ≥ 18 years old and ≤ 75 years old; * Sign on the informed consent; * Diagnosis of: 1. CLL with an indication for treatment based on iwCLL 2018 and measurable disease, or 2. SLL (lymphadenopathy and/or splenomegaly and \< 5×10\^9 CD19+ CD5+ clonal B lymphocytes/L \[\< 5000/µL\] in the peripheral blood at diagnosis with measurable disease that is biopsy-proven SLL); * Relapsed/refractory patients, Subjects must have received and failed Bruton tyrosine kinase inhibitor (BTKi) treatment or have been deemed ineligible for BTKi therapy; * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1; * Expected survival is greater than 12 weeks; * Adequate organ function; * Adequate vascular access for leukapheresis procedure; * Women of childbearing potential must agree to use highly effective methods of contraception for 1 year after the last dose of JWCAR029; Males who have partners of childbearing potential must agree to use an effective barrier contraceptive method for 1 year after the last dose of JWCAR029. Exclusion Criteria: * Central nervous system (CNS) only involvement by malignancy or primary CNS lymphoma; * History of another primary malignancy that has not been in remission for at least 2 years; * Subjects has HBV, HCV, HIV or syphilis infection at the time of screening; * Deep venous thrombosis (DVT)/Pulmonary embolism (PE), or DVT/PE requires anti-coagulation within 3 months prior to signing the ICF; * Subjects with uncontrolled systemic fungal, bacterial, viral or other infection; * Presence of acute or chronic graft-versus-host disease (GVHD); * History of any serious cardiovascular disease or presence of clinically relevant CNS pathology; * Pregnant or nursing women; * Subjects using of any chemotherapy, corticosteriod, experiment agents, GVHD therapies, radiation or any other therapies for lymphoma must go through a specific wash-out period before leukapheresis; * Received allo-hematopoietic stem cell transplantation therapy previously. * Uncontrolled conditions or unwillingness or inability to follow the procedures required in the protocol; * Received CAR T-cell or other genetically-modified T-cell therapy previously.