 Thalassemia is an inherited blood disorder in which the body makes an abnormal form of hemoglobinthe protein in red blood cells that carries oxygen. A potential complication of thalassemia is pulmonary hypertension, which is a condition characterized by abnormally high blood pressure in the arteries of the lungs. People with thalassemia who have pulmonary hypertension tend to experience more health complications, including shortness of breath and a reduced exercise capacity, than people with thalassemia who do not have pulmonary hypertension. Sildenafil is a medication that is used to treat pulmonary hypertension; however, it has not yet been studied in people with thalassemia. The purpose of this study is to evaluate the safety and effectiveness of sildenafil at reducing blood pressure in the lungs of people who have thalassemia and pulmonary hypertension. Study researchers will also further compare the differences between people with thalassemia who have pulmonary hypertension and those who do not have pulmonary hypertension. 