Telaprevir Plus Standard of Care (SOC) in HCV Associated Hepatocellular Carcinoma (HCC)

Study Drug Administration: If you are found to be eligible to take part in this study, you will take telaprevir 3 times a day. You will take RVB by mouth 2 times a day. You will receive PEGIFN alfa-2a by an injection under the skin 1 time a week. Study Visits: On the first day you take the study drug: * You will have an eye exam performed by the study doctor. * You will have a physical exam, including measurement of your vital signs (blood pressure, heart rate, temperature, and breathing rate). * Blood (about 2 teaspoons) will be drawn for routine tests and to check for the hepatitis virus. * You will be asked about any drugs you are taking or side effects you may be having. Every Week while you are on study: * You will have a physical exam, including measurement of your vital signs. * Blood (about 2 teaspoons) will be drawn for routine tests and to check for the hepatitis C virus. If part of the blood sample is left over after the Hepatitis C testing, it will be stored in the laboratory as a back-up sample, in case the original samples get lost. This sample may also be used to check if the Hepatitis C virus has become resistant to the study drug. No extra blood will be drawn for this storage. * You will be asked about any drugs you are taking or side effects you may be having. * At Weeks 12, 24, 36, and 42, urine will be collected to check for infection and any other side effects to the drugs. If you can become pregnant, you will have a urine pregnancy test every 4 weeks Length of Treatment: You may continue receiving the antiviral therapy for up to 48 weeks, as long as the doctor thinks it is in your best interest. You will no longer be able to take the study drug if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions. Your participation on the study will be over after the follow-up visits. Follow-Up Visits: Beginning the day after you stop taking antiviral therapy (or the day of transplantation, whichever comes first), you will have up to 24 weeks of follow-up testing performed. About 4 and 20 weeks after your last dose: * You will have a physical exam, including measurement of your vital signs. * Blood (about 2 teaspoons) will be drawn for routine tests and to check for the hepatitis C virus. * You will be asked about any side effects you may be having. * At week 4 only, urine will be collected to check for infection and any other side effects to the drugs. This is an investigational study. Telaprevir, PegIFN alfa-2a, and RBV are all FDA approved and commercially available for the treatment of HCV infection. The use of these drugs in preventing the HCV infection is investigational. Up to 40 patients will take part in this study. All will be enrolled at MD Anderson.