This 12-month study will evaluate the safety and effectiveness of hydroxyurea in treating beta-thalassemia, a type of anemia caused by defective hemoglobin (the oxygen-carrying pigment in blood). Hemoglobin is composed of two protein chains-alpha globin chains and beta globin chains; patients with beta-thalassemia do not make beta globin. Patients often require frequent red blood cell transfusions. This leads to iron overload, which, in turn, requires iron chelation therapy (removal of iron from the blood).