This is a randomized, multi-site, open-label trial of a fixed-dose combination of Grazoprevir (MK-5172) and Elbasvir (MK-8742) versus Boceprevir (BOC) / Pegylated Interferon (P) and Ribavirin (R) in treatment-naive and prior treatment failure genotype (GT) 1 hepatitis C virus (HCV)-infected participants. The primary hypothesis is that the proportion of treatment-naive (TN) and prior treatment failure (PTF) participants treated with grazoprevir + elbasvir achieving sustained virologic response (undetectable HCV ribonucleic acid [RNA]) 12 weeks after the end of study therapy (SVR12) will be greater than the proportion of BOC/PR-treated participants achieving SVR12.

Inclusion Criteria:

• Has HCV RNA ≥ 10,000 IU/mL at the time of screening
• Has documented chronic HCV GT 1 with no evidence of non-typeable or mixed GT infection
• Is cirrhotic or non-cirrhotic
• Has HCV treatment status that is treatment naïve, PR null responder; PR partial responder; or prior PR relapser
• If human immunodeficiency virus (HIV) co-infected (HIV-1) must be naïve to treatment with any antiretroviral therapy (ART) and have no plans to initiate ART treatment while participating in this trial, or be on HIV ART for at least 8 weeks prior to trial entry (no changes in HIV regimen are allowed within 4 weeks of registration); must also have at least one viable antiretroviral therapy alternative beyond their current regimens in the event of HIV virologic failure and the development of antiretroviral drug resistance
• Use an acceptable method of contraception or not be of childbearing potential

Exclusion Criteria:

• Has evidence of decompensated liver disease manifested by the presence of or history of ascites, esophageal or gastric variceal bleeding, hepatic encephalopathy or other signs or symptoms of advanced liver disease
• Is co-infected with hepatitis B virus (e.g., hepatitis B surface antigen [HBsAg] positive)
• Has a history of malignancy ≤5 years prior to signing informed consent except for adequately treated basal cell or squamous cell skin cancer or in situ cervical cancer or carcinoma in situ; or is under evaluation for other active or suspected malignancy
• Has cirrhosis and liver imaging within 6 months of Day 1 showing evidence of hepatocellular carcinoma (HCC) or is under evaluation for HCC
• Has pre-existing psychiatric condition(s)
• Has clinically-relevant drug or alcohol abuse within 12 months of screening
• Is a female and is pregnant or breast-feeding, or expecting to become pregnant or donate eggs from Day 1 throughout treatment and until at least 6 months after the last dose of study medication, or longer if dictated by local regulations; or is a male subject and is planning to impregnate or provide sperm donation
• Has any preexisting condition or prestudy laboratory abnormality, electrocardiogram (ECG) abnormality or history of any illness, which, in the opinion of the investigator, might confound the results of the trial or pose additional risk in administering the study drug(s) to the subject
• Has a life-threatening severe AE (SAE) during the screening period
• Has evidence of history of chronic hepatitis not caused by HCV, including but not limited to nonalcoholic steatohepatitis (NASH), drug-induced hepatitis, and autoimmune hepatitis