This study will enroll HIV-1-infected children less than 12 years of age who are naive to antiretroviral therapy (ART) (have never taken ARV drugs). Study participants will be assigned to 1 of 2 cohorts based on age. Cohort 1 will include children at least 6 years of age to less than 12 years of age. Cohort 2 will include children at least 2 years of age to less than 6 years of age. Each cohort will consist of two stages: Stage 1 and Stage 2. Stage 1 will be the initial dose finding stage. Participants will begin treatment with daily RPV and 2 nucleoside reverse transcriptase inhibitors (NRTIs). The 2 NRTIs will be selected by the site investigator but will not be provided through the study. This stage of the study will involve intense pharmacokinetic (PK) sampling to evaluate the safety, tolerability, and antiviral activity of RPV, which will allow for the selection of an RPV dose to use in Stage 2 of the study. Participants in both cohorts will remain on RPV-based therapy for up to 48 weeks.