CD19-specific T-cell for Chronic Lymphocytic Leukemia (CLL)

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.