An Efficacy and Safety Study of Grazoprevir (MK-5172) + Elbasvir (MK-8742) in the Treatment of Chronic Hepatitis C Virus (HCV) Genotype (GT)1, 4, or 6 Infection in Treatment-Naïve Participants Who Are on Opiate Substitution Therapy (MK-5172-062)

Inclusion Criteria: Part A * Documented chronic HCV GT1, GT4, or GT6 infection with no evidence of GT2, GT3, GT5 or non-typeable genotypes and HCV ribonucleic acid (RNA) confirmed by screening lab results prior to randomization * On opiate substitution therapy (OST; methadone, levamethadone, buprenorphine, naloxone, naltrexone) for at least 3 months prior to screening * Treatment naïve to all HCV therapies * Human Immunodeficiency Virus (HIV)-infected participants enrolled in this study must meet following criteria: * Documented HIV infection * Naïve to treatment with any antiretroviral therapy (ART) OR on HIV ART for at least 8 weeks prior to study entry using a dual nucleoside reverse transcriptase inhibitor (NRTI) backbone of tenofovir or abacavir and either emtricitabine or lamivudine PLUS raltegravir (or dolutegravir or rilpivirine). Dose modifications or changes in ART during the 4 weeks prior to study entry (Day 1) are not permitted * Cluster of differentiation 4 (CD4+) T-cell count \>200 cells/mm\^3 if on ART or \>500 cell/mm\^3 if ART treatment naïve * Undetectable plasma HIV-1 RNA at least 8 weeks prior to screening if on ART or \<50,000 copies/mL if ART treatment naïve * Participants with HIV-1 infection and on ART must have at least one viable antiretroviral regimen alternative beyond their current regimen in the event of HIV virologic failure or the development of anti-retroviral drug resistance * Females who are of reproductive potential must agree to avoid becoming pregnant while receiving study drug and for 14 days after the last dose of study drug by complying with one of the following: (1) practice abstinence from heterosexual activity OR (2) use (or have her partner use) acceptable contraception during heterosexual activity Part B * Received at least one dose of grazoprevir in combination with elbasvir in Part A. Receiving OST and keeping \>80% of scheduled appointments while on OST were not required for Part B. Exclusion Criteria: Part A * Evidence of decompensated liver disease * For participants with cirrhosis, participants who are Child-Pugh Class B or C or who have a Pugh-Turcotte (CPT) score \>6 * Is co-infected with hepatitis B virus * Has cirrhosis and liver imaging within 6 months of Day 1 showing evidence of hepatocellular carcinoma (HCC) or is under evaluation for HCC * Currently using or intends to use barbiturates during the treatment period of this study * Is a female and is pregnant or breast-feeding, or expecting to conceive or donate eggs from Day 1 or anytime during treatment, and 14 days after the last dose of study medication, or longer if dictated by local regulations * Any medical condition requiring or likely to require chronic systemic administration of corticosteroids, Tumor Necrosis Factor (TNF) antagonists, or other immunosuppressant drugs during the course of the trial * Evidence or history of chronic hepatitis not caused by HCV Part B * Mentally or legally incapacitated, has significant emotional problems at the time of pre-study screening visit or expected during the conduct of the study or has a history of a clinically significant psychiatric disorder which, in the opinion of the investigator, would interfere with the study procedures * Has a medical condition or personal circumstance which, in the opinion of the investigator and/or Sponsor, places the participant at unnecessary risk through continued participation in the trial or does not allow the participant to adhere to the requirements of the protocol