This is a randomized, double-blind, placebo-controlled Phase III trial with telaprevir in patients with chronic Hepatitis C Virus (HCV), genotype 1, infection who failed prior treatment with standard treatment. Standard treatment is defined as treatment with Peg-INF and RBV. The trial is designed to compare the efficacy, safety, and tolerability of 2 regimens of telaprevir (with and without delayed start) combined with standard treatment versus standard treatment alone. The trial will consist of a screening period of approximately 4 weeks, a 48-week treatment period, and a 24-week follow-up period. Patients will be eligible to enroll in the trial if they (1) had an undetectable HCV Ribonucleic Acid (RNA) level at the end of a prior course of standard treatment but did not achieve a response (viral relapsers), or (2) never had an undetectable HCV RNA level during or at the end of a prior course of standard treatment (non-responders). Approximately 650 patients (350 prior relapsers and 300 prior non-responders) will be randomized in a 2:2:1 ratio to one of 3 treatment groups: Treatment group A will receive telaprevir with standard treatment for 12 weeks; followed by placebo with standard treatment for 4 weeks; followed by standard treatment for 32 weeks. Treatment group B will receive placebo with standard treatment for 4 weeks; followed by telaprevir with standard treatment for 12 weeks; followed by standard treatment for 32 weeks. Treatment group C will receive placebo with standard treatment for 16 weeks; followed by standard treatment for 32 weeks. In both telaprevir regimens (A and B), patients will receive 12 weeks of 750 mg of telaprevir every 8 hours along with 48 weeks of standard treatment. Telaprevir or placebo will be given by mouth at a dose of 750 mg every 8 hours for 16 weeks. Peg-INF will be given as an injection under the skin at a dose of 180 mcg once every week for 48 weeks. RBV will be given by mouth at a dose of either 1000 or 1200 mg (depending on your body weight) two times per day for 48 weeks.