This study will evaluate the safety and effectiveness of 5-azacytidine and phenylbutyrate for treating thalassemia major. Patients with this disease have abnormal production of hemoglobin (the oxygen-carrying protein in red blood cells), which leads to red blood cell destruction. As a result, patients require frequent red cell transfusions over many years. Because of these transfusions, however, excess iron is deposited in various body organs-such as the heart, liver, thyroid gland and, in men, the testes-impairing their function.