Key Inclusion Criteria:

          -  Documentation of relapsed or refractory CLL and SLL; must have received at least 2
             prior lines of treatment, one of which must include a Bruton's tyrosine kinase (BTK)
             inhibitor.

               -  Cohort 1 and 2: Subjects with r/r CLL who have received at least 2 prior lines of
                  treatment, one of which must include a BTK inhibitor.

               -  Cohort 3: Subjects with r/r CLL and SLL must present with ≤ 1% circulating tumor
                  cells in peripheral blood or ALC < 5000 cells/μL. Subjects must have received at
                  least 2 prior lines of treatment, one of which must include a BTK inhibitor.

               -  Cohort 4: Subjects with r/r CLL who have received at least 2 prior lines of
                  treatment and must have received ibrutinib as a single agent or in comibation
                  with anti-CD20 antibodies, BCL-2 inhibitors, and PI3k inhibitors for at least 6
                  months as the last line of therapy prior to screening. Ibrutinib administration
                  will continue up to 30 hours prior to leukapheresis. In case of treatment
                  interruption with ibrutinib, the principal investigator should reach out to the
                  medical monitor to discuss.

          -  An indication for treatment per IWCLL 2018 criteria and radiographically measurable
             disease (at least 1 lesion > 1.5 cm in diameter)

          -  Adequate hematologic function as indicated by:

               -  Platelet count ≥ 50 × 10^9/L

               -  Neutrophil count ≥ 0.5 × 10^9/L

               -  Hemoglobin ≥ 8 g/dL unless lower values are attributable to CLL

          -  Adequate renal, hepatic, cardiac and pulmonary function defined as:

               -  Creatinine clearance (as estimated by Cockcroft-Gault) ≥ 60 mL/min

               -  Serum alanine aminotransferase (ALT)/aspartate aminotransferase (AST) ≤ 2.5 x
                  upper limit of normal (ULN)

               -  Total bilirubin ≤ 1.5 mg/dL unless subject has Gilbert's syndrome

               -  Left ventricular ejection fraction (LVEF) ≥ 50%, no evidence of pericardial
                  effusion, no New York Heart Association (NYHA) class III or IV functional
                  classification, no clinically significant arrhythmias

               -  No clinically significant pleural effusion

               -  Baseline oxygen saturation > 92% on room air

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1

          -  At least 2 weeks or 5 half-lives, whichever is shorter, must have elapsed since any
             prior systemic therapy or BTKi (ibrutinib or acalabrutinib) at the time the subject is
             planned for leukapheresis, except for systemic inhibitory/stimulatory immune
             checkpoint therapy. At least 3 half-lives must have elapsed from any prior systemic
             inhibitory/stimulatory immune checkpoint molecule therapy at the time the subject is
             planned for leukapheresis (eg, ipilimumab, nivolumab, pembrolizumab, atezolizumab,
             OX40 agonists, 4-1BB agonists)

        Key Exclusion Criteria:

          -  A history of treatment including any of the following:

               -  Prior CD19 directed therapy

               -  Prior allogeneic hematopoietic stem cell transplant (SCT) or donor lymphocyte
                  infusion (DLI) within 6 months prior to enrollment

          -  History of autoimmune disease resulting in end-organ injury unless attributable to CLL
             (eg, idiopathic thrombocytopenic purpura (ITP), autoimmune hemolytic anemia (AIHA))

          -  Diagnosis of Richter's transformation or a history of malignancy other than
             non-melanoma skin cancer or carcinoma in situ (eg, skin, cervix, bladder, breast),
             superficial bladder cancer, asymptomatic localized low grade prostate cancer for which
             watch-and-wait approach is standard of care, or any other cancer that has been in
             remission for > 3 years prior to enrollment

          -  History of severe hypersensitivity reaction attributed to aminoglycosides

        Note: Other protocol defined Inclusion/Exclusion criteria may apply.