This study will enroll adults with thalassemia and long-term hepatitis C. Participants will attend study visits weekly for 4 weeks, every 2 weeks until Week 24, every 4 weeks until Week 48, and then every 6 weeks until Week 72. All participants will receive a peginterferon alfa-2a injection once a week and ribavirin daily. Participants with the hepatitis C genotype 1 will receive 48 weeks of treatment; participants with all other genotypes of the disease will receive 24 weeks of treatment. A liver biopsy will occur at baseline and Week 48. The following will occur at selected study visits: physical exam, blood and urine collection, hearing and vision screening, chest x-ray, heart rate monitoring, and questionnaires to assess hepatitis C symptoms, quality of life, and depression. Participants with liver iron levels greater than 20 mg/g will undergo an echocardiogram ultrasound test every 3 months to monitor the heart.