This study will provide vaniprevir 600 mg or 300 mg twice daily in combination with pegylated interferon (peg-IFN) and ribavirin (RBV) to participants with chronic hepatitis C virus (HCV) infection who did not achieve viral eradication while participating in a prior vaniprevir clinical trial (MK-7009-004, NCT00518622; MK-7009-007, NCT00704405; MK-7009-009, NCT00704184; and MK-7009-029, NCT00954993).