The main goals of this study is to determine the safety and appropriate dose of these modified T cells in patients with ALL. This will be done in a "clinical trial." The dose of modified T-cells will depend on if you have disease present in your bone marrow or not. The patient will also receive chemotherapy before the T cells. We will use normally chemotherapy that is used in patients with leukemia. The chemotherapy is given to reduce leukemia and to allow the T cells to live longer.