This study will enroll HCV genotype 1a or 1b and HIV-1 coinfected participants (HCV treatment-naïve or HCV treatment-experienced) who are on a concurrent integrase inhibitor (INI)-based (raltegravir [RAL] or dolutegravir [DTG]) or protease inhibitor (PI)-based (darunavir [DRV] or atazanavir [ATV]) ART regimen. (The ART regimens will not be provided by the study.) The participants will be assigned to one of four cohorts (Cohorts A, B, C, and D). Participants in Cohorts A and B will be on INI-based ART; participants in Cohorts C and D, on PI-based ART. For each group, the study will proceed in two steps: Step 1: on-HCV treatment and Step 2: post-HCV treatment follow-up. Participants in Cohorts A and C will receive the HCV drugs for 24 weeks; participants in Cohorts B and D, for 12 weeks.