Pilot Study of Autologous T Lymphocytes With ADCC in Patients With CD20-Positive B-Cell Malignancies

Inclusion Criteria: 1. Age: 6 months to 80 years old. 2. i) Diagnosis of aggressive CD20+ B-NHL with measurable tumor burden (by imaging, flow cytometry and/or PCR) post-treatment. This includes patients with persistent disease following more than 2 lines of chemotherapy, as well as patients who relapse following autologous transplantation, and in whom further salvage therapy has produced only a partial remission or where no effective salvage therapy available. Patients with bulky disease who require immediate salvage therapy will not be eligible. OR ii) Diagnosis of poor risk indolent CD20+ B-NHL or Chronic Lymphocytic Leukemia. This includes high risk CLL cases with early relapse (\<12 months following purine analog containing treatment or \<24 months following autologous transplant), or with 17p deletion needing treatment, and who are not candidates (or refuses) allogeneic transplantation. Patients with advanced progressive indolent B-NHL with relapsed, refractory disease who have failed more than 2 lines of treatment (including autologous transplantation) may also be considered. 3. Shortening fraction greater than or equal to 25%. 4. Glomerular filtration rate greater than or equal to 50 ml/min/1.73 m2. 5. Pulse oximetry greater than or equal to 92% on room air. 6. Direct bilirubin less than or equal to 3.0 mg/dL (50 mmol/L). 7. Alanine aminotransferase (ALT) is no more than 2 times the upper limit of normal unless determined to be directly due to disease. 8. Aspartate transaminases (AST) is no more than 2 times the upper limit of normal unless determined to be directly due to disease. 9. Karnofsky or Lansky performance score of greater than or equal to 50. 10. No clinical history of or overt autoimmune disease. 11. No past history of previous severe adverse reactions to rituximab, eg. cytokine release syndrome 12. Has recovered from all acute NCI Common Toxicity Criteria grade II-IV non-hematologic acute toxicities resulting from prior therapy per the judgment of the PI. 13. Is not receiving more than the equivalent of prednisone 10 mg daily. 14. Not pregnant (negative serum or urine pregnancy test to be conducted within 7 days prior to enrollment). 15. Not lactating. Exclusion Criteria: Failure to meet any of the inclusion criteria