In this study, all patients will receive open-label (all people involved know the identity of the intervention) telaprevir in addition to Peg IFN-alfa and RBV for treatment of hepatitis C virus (HCV) and protocol permissible treatments for HIV. Chronic hepatitis C infection causes inflammation of the liver which can potentially cause long-term complications of the current liver disease (fibrosis or cirrhosis). Therefore it is important the patient is treated for this infection. Telaprevir is an experimental medication that has been tested for the treatment of hepatitis C infections in several previous studies in more than 2500 patients. Telaprevir is a member of a new class of drugs being developed for chronic hepatitis C: Direct Acting Antiviral (DAA) agents. Unlike pegylated interferon (Peg-IFN) and ribavirin (RBV), DAA agents act directly on the hepatitis C virus (HCV) replication cycle. The aim of the telaprevir treatment is to eradicate the Hepatitis C virus out of the patient's body. This can be measured by testing the amount of a certain part of this Hepatitis C virus, called the Ribonucleic acid (RNA \[HCV RNA\]) in their blood. It is possible that the patient will not respond to the therapy and the levels of HCV RNA in their blood will not decrease or even increase. Based on these results it might be decided the patient will not benefit from treatment and he/she need to stop the telaprevir only or all medication for their hepatitis C infection. The doctor will keep them informed about the patient's reaction to the treatment and will take the necessary measurements as prescribed by the study protocol and routine medical practice. During the study the patient will simultaneously be treated with the therapy that the doctor would normally prescribe for treatment of their chronic hepatitis C infection: "ribavirin (RBV)" and "pegylated interferon alfa (PEG-INF-alfa)". Telaprevir is always administered in combination with RBV and PEG-IFN-alfa. In function of the patient's specific HIV status, the doctor has prescribed, or not, a specific treatment that the patient will continue to take during the study. This treatment could be: (a) efavirenz, tenofovir disoproxil fumarate (TDF), plus either emtricitabine or lamivudine, (b) efavirenz, abacavir, plus either emtricitabine or lamivudine, (c) ritonavir-boosted atazanavir, TDF, plus either emtricitabine or lamivudine, (d) ritonavir-boosted atazanavir, abacavir, plus either emtricitabine or lamivudine, (e) raltegravir, TDF, plus either emtricitabine or lamivudine, (f) raltegravir, abacavir, plus either emtricitabine or lamivudine or (g) etravirine, TDF, plus either emtricitabine or lamivudin, (h) etravirine, abacavir, plus either emtricitabine or lamivudine, (i) rilpivirine, TDF, plus either emtricitabine or lamivudine, (j) rilpivirine, abacavir, plus either emtricitabine or lamivudine, (k) no treatment. In an interim analysis of a Phase 2a study, human immunodeficiency virus (HIV)-1/HCV genotype 1 coinfected patients currently receiving HIV therapy who had telaprevir added to Peg IFN-alfa-2a and RBV regimen for treatment of their HCV genotype 1 infection had a higher HCV RNA response (undetectable HCV RNA) at Weeks 4 and 12 than those who received only the Peg-IFN-alfa-2a and RBV regimen. These responses were sustained through Week 24, with 73.7% of patients who had telaprevir added to the Peg-IFN-alfa-2a and RBV regimen and 54.5% of patients who received only the Peg-IFN-alfa-2a and RBV regimen also achieving undetectable HCV RNA at Week 24. Patients with severe fibrosis or cirrhosis have a lower likelihood of sustained virologic response (SVR) and also have the greatest risk of liver failure, hepatocellular carcinoma (HCC), and death. Administering telaprevir in this difficult to treat population may reduce the risk of long-term complications associated with HCV in patients with HIV/HCV genotype 1 coinfection. All patients eligible to enter the study will receive telaprevir (750 or 1,125 mg every 8 hours based on their Highly Active Antiretroviral Therapy (HAART) regimen) during the first 12 weeks of the study in combination with Peg IFN alfa/RBV. Patients will subsequently be treated with Peg-IFN-alfa/RBV for an additional 36 weeks. The total duration of Peg-IFN-alfa/RBV will be 48 weeks. HCV RNA levels should be measured at Weeks 4, 12, 24 and 48. All patients should have a posttreatment follow-up visit, including measurement of plasma HCV RNA levels, performed 24 weeks after the last administered dose of treatment. Note that in certain countries, an additional main objective of the study is to provide Early Access to telaprevir in this population.