The reason for doing this study is to determine whether a new method of blood stem cell transplant (also known as bone marrow transplant) is able to treat acute lymphocytic leukemia. Blood stem cells are the "seed cells" necessary to make all blood cells. This new method of transplant uses a combination of low dose radiation and chemotherapy that may be less toxic and cause less harm than a conventional transplant. This lower dose transplant is called a "nonmyeloablative transplant". Researchers want to see if using less radiation and less chemotherapy combined with new immune suppressing drugs after the transplant will help a stem cell transplant to work. Researchers hope that this treatment will cure acute lymphocytic leukemia with fewer side effects. Researchers are hoping to see a mixture of recipient and donor blood cells after transplant. This mixture of donor and recipient blood cells is called "mixed chimerism". Researchers hope that donor cells will attack and eliminate the leukemia. This is called the "graft-versus-leukemia" effect. In addition, after the transplant, white blood cells from the donor may be given to enhance or "boost" the graft-versus-leukemia effect, and hopefully remove all remaining cancer cells. This study is being done because at the present time blood stem cell transplantation (or bone marrow transplantation) is the only known curative therapy for acute lymphocytic leukemia. Because of age or underlying health status acute lymphocytic leukemia patients have a higher likelihood of experiencing severe harm from a conventional blood stem cell transplant. Researchers are doing this study to see if this new nonmyeloablative method of low dose radiation and low dose chemotherapy given before transplant and immune suppressive drugs after transplant will help make the transplant safer and also cure acute lymphocytic leukemia