This is a 2-part study. The purpose of Part A is to assess the efficacy and safety of grazoprevir (MK-5172) 100 mg in combination with elbasvir (MK-8742) 50 mg for 12 weeks in the treatment of chronic hepatitis C virus (HCV) genotype 1 (GT1), GT4, or GT6 infection in treatment-naïve participants who are on opiate substitution therapy (OST). The primary hypothesis is that the percentage of participants who receive grazoprevir/elbasvir fixed-dose combination (FDC) in the Immediate Treatment Arm and achieve a Sustained Virologic Response 12 weeks after the end of all study therapy (SVR12) will be superior to 67%. In addition, participants who received at least 1 dose of grazoprevir/elbasvir in Part A will be eligible to participate in Part B, which is a 3-year observational follow-up.