Chronic hepatitis C infection is one of the leading causes of chronic liver disease in the United States. Approximately one-third of patients with hepatitis C infection develop cirrhosis of the liver, which can lead to liver failure or liver cancer. The current treatment for hepatitis C infection in previously untreated patients is successful in only about half of patients. There is no established therapy for non-responders. This is a randomized, double-blinded, multicenter trial to determine the effectiveness of thymosin alpha 1 (thymalfasin) 1.6 mg twice weekly plus PEGinterferon alfa-2a 180 ug/wk compared to placebo plus PEGinterferon alfa-2a in adults with chronic hepatitis C without cirrhosis who are non-responders to previous treatment with interferon or interferon plus ribavirin. The definition of non-response requires a positive HCV RNA test at the end of a course of at least 12 weeks of therapy. Patients will receive treatment for 12 months, and will be followed-up for a further 6 months after the end of therapy.