Hepatitis C virus (HCV) infection is a world wide public health concern and is the most common chronic bloodborne infection in the United States and the leading indication for liver transplantation. Laboratory and animal studies have demonstrated that bavituximab binds viruses and virally infected cells and prolongs survival in infected animals. This study will examine the safety and tolerability of bavituximab when administered to patients with chronic HCV infection who do not respond to or relapse after treatment with pegylated interferon plus ribavirin combination therapy. Groups of patients will be treated with escalating doses and followed for 12 weeks.