Hepatitis C is an inflammation of the liver that is caused by infection with the hepatitis C virus. Over time, people may develop liver failure, liver cancer, or cirrhosis, a condition in which the liver may become permanently scarred. Ribavirin and peginterferon alfa-2a are two medications that are used to treat hepatitis C. Ribavirin stops the hepatitis C virus from spreading inside the body, and peginterferon alfa-2a decreases the amount of hepatitis C virus in the body. Individuals with thalassemia, an inherited blood disorder that can cause anemia, often receive regular blood transfusions as part of their treatment. These individuals may have an increased risk of developing hepatitis C as a result of blood transfusions received before routine hepatitis C blood screening was available. Treating thalassemia patients with standard hepatitis C therapy can be difficult because ribavirin can worsen anemia. However, omitting ribavirin then increases the risk of hepatitis C relapse following treatment. The purpose of this study is to evaluate the safety of ribavirin and peginterferon alfa-2a for treating hepatitis C in adults with thalassemia.