A Phase I Extension Trial of Repeated Infusions of ISF35

Inclusion Criteria:

1. Subjects must have been enrolled and tolerated the single dose ISF35 in MDACC Protocol 2004-0914.
2. Subjects must have adequate Ad-ISF35 transduced CLL B cells to allow for at least one additional treatment.
3. Women of childbearing potential (not postmenopausal for at least one year or not surgically incapable of bearing children) must agree not to become pregnant for the duration of the study. Both men and women participants must agree to use contraception for the duration of the study.
4. Subjects must have Zubrod performance status of ≤ 2.
5. Subjects must have adequate hematologic, renal, hepatic, and coagulation function:

   * Adequate hematologic function:

     * Platelet count ≥ 50,000/μl; AND
     * Hemoglobin ≥ 10 g/dl (may be supported by erythropoietin or transfusion).
   * Adequate renal function:

     * Serum creatinine ≤ 1.5 times upper limit of normal; OR
     * Measured creatinine clearance ≥ 40 mL/min/1.73 m\^2.
   * Adequate hepatic function:

     * Total bilirubin ≤ 2.5 times upper limit of normal; AND
     * ALT ≤ 2.5 times upper limit of normal; AND
   * Adequate coagulation tests:

     * Prothrombin time international normalized ratio (INR) ≤ 2; AND
     * Partial thromboplastin time ≤ 1.66 times upper limit of normal
6. Subjects must give written informed consent for the Phase 1B extension trial.

Exclusion Criteria:

1. Unresolved toxicity (Grade ≥ 2) from single administration of Add-ISF35 transduced autologous CLL B cells.
2. Presence of more than 55% prolymphocytes.
3. Chemotherapy (e.g., purine analogues, alkylating agents, or corticosteroids), antibody therapy, immunotherapy, radiation therapy, or participation in any investigational drug treatment within 4 weeks of enrollment into protocol or at any time during the study.
4. Ongoing toxicity from prior anti-neoplastic therapy.
5. Prior gene therapy (EXCEPT Ad-ISF35) or allogeneic stem cell transplantation.
6. Untreated autoimmune hemolytic anemia or immune thrombocytopenia.
7. Active infection requiring parenteral antibiotics.
8. HIV/HBV/HCV seropositivity.
9. Uncompensated hypothyroidism (defined as TSH greater than 4x upper limit of normal not treated with replacement hormone).