The goal of this clinical research study is to find the highest tolerable dose of T cells that can be given in combination with standard chemotherapy to patients with CLL. The safety of this combination will also be studied.

The T cells being used in this study are a type of white blood cell that will be taken from your blood and then genetically changed in a laboratory. The process of changing the DNA (the genetic material of cells) of the T cells is called a gene transfer. After the gene transfer is complete, the genetically changed T-cells will be put back into your body. These T cells may help prevent cancer cells from coming back.

Study Groups:

If you are found to be eligible to take part in this study, you will be assigned to a dose level of genetically changed T cells, based on when you joined this study. Up to 4 dose levels of T cells will be tested. Up to 3 participants will be enrolled at each dose level. The first group of participants will receive the lowest dose level. Each new group will receive a higher dose of than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of T cells is found.

All participants will receive the same dose of chemotherapy.

T Cell Collection (leukapheresis or standard blood draw):

Within 30 days after you have completed the screening tests, you will have leukapheresis performed at the Apheresis Clinic at MD Anderson.

Before the leukapheresis:

• You will have a physical exam, including measurement of your height, weight, and vital signs.
• Your medical history will be recorded.
• Blood (about 4 tablespoons) will be drawn for routine tests and to measure levels of certain proteins.

A leukapheresis is a procedure used to remove blood from the body so that specific blood cells, such as T cells, can be collected. After the specific cells have been collected, the remaining blood is returned to the body.

To perform a leukapheresis, blood will be drawn through a needle in a vein in one arm, then passed though a machine to collect white blood cells, and then the remaining blood will be returned back to you through a needle in a vein in the other arm. The procedure will take about 3 hours to complete.

If the doctor thinks it is in your best interest, instead of having a leukapheresis, blood (about 13.5 tablespoons) will be drawn to collect white blood cells instead.

If certain types of unwanted T cells are growing too much, an investigational device called a CliniMACS® system will be used to filter out the unwanted T cells using a magnet.

It will take about 7 weeks to modify and grow the necessary number of genetically modified T cells in the lab. If researchers are not able to collect enough T cells for your assigned dose level, you will be taken off study. Other options will be discussed with you by your doctor.

Chemotherapy:

Before you receive the T cell infusion, you will receive your standard chemotherapy with fludarabine and cyclophosphamide through a catheter (plastic tube) inserted into a large chest vein or through an intravenous needle (IV) inserted in a vein in your arm.

Fludarabine will be given by vein over 30 minutes daily for 3 days.

Cyclophosphamide will be given by vein over 3 hours daily for 3 days.

Study Tests Before the T cell Infusion:

Within 60 days before the T cell infusion:

• You will be asked about any side effects that you may have had.
• Blood (about 2 tablespoons) will be drawn for tests to look at your DNA to check the status of the disease. This may be performed any time before or during the study.
• Mouse protein antibodies are used in the gene transfer process. If your body becomes immune to these proteins, your body may develop antibodies against the mouse antibodies (called "human anti-mouse antibodies" or HAMA). Part of the blood sample will be used to compare against another sample of blood collected after the gene transfer is complete to check for HAMA.
• You will have an echocardiogram (ECHO) or multigated acquisition (MUGA) scan to check your heart function.
• You will have lung function tests.
• If the study doctor thinks it is needed, you will have a bone marrow biopsy/aspiration to check the status of the disease. To collect a bone marrow biopsy/aspirate, an area of the hip or chest bone is numbed with anesthetic, and a small amount of bone and bone marrow is withdrawn through a large needle.
• If the study doctor thinks it is needed, you will have computed tomography (CT) scans and/or positron emission tomography (PET) scans to check the status of the disease.

Within 7 days before starting chemotherapy:

• You will have a physical exam, including measurement of your weight, and vital signs.
• Your medical history will be reviewed and any updates will be recorded.
• You will be asked about any side effects that you may have had.
• Blood (about 2 tablespoons) will be drawn for routine tests. Part of this blood sample will be used for a pregnancy test if you are able to become pregnant. To continue your participation in this study, you cannot be pregnant.

T-cell Infusion (gene transfer):

The T cell infusion will be given by vein over about 15-30 minutes.

Before the infusion, you will receive drugs to lower your risk of allergic reaction to the T cells. Tylenol® (acetaminophen) will be given by mouth and Benadryl® (diphenhydramine) may be given by mouth or by vein over a few minutes.

Your vital signs will be checked during and after the T cell infusion.

Study Tests after the T cell infusion:

Within 3 days, 1 week (+/- 2 days), 2 weeks (+/- 3 days), 1 month (+/- 7 days), 6 months (+/- 14 days), and 12 months (+/- 14 days) after the T-cell infusion, the following tests and procedures will be performed:

• You will have a physical exam, including measurement of your weight and vital signs.
• Your medical history will be reviewed and any updates will be recorded.
• You will be asked about any side effects that may have had.
• Blood (about 4 tablespoons) will be drawn for routine tests, tests to measure levels of certain proteins, and tests to look at your DNA to check the status of the disease. Part of this blood sample will be used to compare against a sample of blood that was collected before the gene transfer to check for HAMA (at 6 months after the T cell infusion only). At 1, 6, and 12 months after the T-cell infusions, part of this blood sample will be used to measure levels of certain proteins.
• Blood (about 4 tablespoons) will be drawn to learn how your body's immune system responds to the T-cell infusion.

At around 6 and 12 months after the T-cell infusion, if the study doctor thinks it is needed you will have CT scans, PET-CT scans, and/or a bone marrow biopsy to check the status of the disease.

Length of Study:

Your participation on this study will be over after you have completed the last planned study visit at about 12 months after the T cell infusion is complete. You may be taken off study early if the disease gets worse, you experience any intolerable side effects, you cannot keep your appointments, if your doctor thinks it is in your best interest, or if you are unable to receive the T-cell infusion.

If you leave the study early for any reason and you received T-cells, if possible, blood (about 2 teaspoons) will be collected. This blood sample will be used to compare against another sample of blood collected after the gene transfer is complete to check for HAMA.

Long-Term Follow-Up Study:

For safety reasons, the U.S. Food and Drug Administration (FDA) requires that patients who receive stem cells infusions that have been treated with a gene transfer procedure must have long-term follow-up for at least 15 years after receiving the gene transfer. You will be asked to sign a separate consent form for a long-term follow-up study Protocol 2006-0676.

This is an investigational study. Fludarabine and cyclophosphamide are commercially available and FDA approved for the treatment of CLL. The T cell infusion using a gene transfer procedure is not commercially available or FDA approved. At this time, T cell infusions using a gene transfer procedure is only being used in research.

Up to 30 patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Patients with a history of B-CLL, who have received at least 2 lines of standard chemoimmunotherapy and have persistent disease.
2. Confirmed history of CD19 positivity by flow cytometry.
3. At least 8 weeks from last cytotoxic chemotherapy. Patients may continue ibrutinib or lenalidomide. These drugs will be discontinued 1 week prior to start of lymphodepleting chemotherapy.
4. Karnofsky Performance Scale > 60%.
5. Absolute lymphocyte count >100/uL.
6. Adequate hepatic function, as defined by serum glutamate pyruvate (SGPT) <3 x upper limit of normal; serum bilirubin and alkaline phosphatase <2 x upper limit of normal, or considered not clinically significant by the study doctor or designee.
7. Able to provide written informed consent.
8. 18-80 years of age.
9. Patient or patient's legal representative, parent(s) or guardian able to provide written informed consent for the long-term follow-up gene therapy study.

Exclusion Criteria:

1. Positive beta human chorionic gonadotropin (HCG) in female of child-bearing potential defined as not post-menopausal for 12 months or no previous surgical sterilization or lactating females.
2. Patients with known allergy to bovine or murine products.
3. Positive serology for HIV.
4. Presence of autoimmune phenomenon (AIHA, ITP) requiring steroid therapy.
5. Presence of Grade 3 or greater toxicity from the previous treatment.
6. Concomitant use of other investigational agents (ibrutinib or lenalidomide are allowed).