The first step in developing gene transfer for treatment of thalassemia is to develop a safe and effective method to obtain blood stem cells from thalassemia patients. Eventually, high numbers of genetically modified cells will need to be infused into the patient for clinical gene transfer to be effective. The blood stem cells are obtained by giving a "mobilization" agent to the patients. This causes the stem cells to leave the bone marrow and go into the blood. The purpose of this study is to test the safety and effectiveness of the new mobilization agent, Mozobil, in causing mobilization of blood stem cells for patients with beta-thalassemia major.