HIV-1-infected cells that persist despite antiretroviral therapy (ART) are frequently considered "transcriptionally silent," but active viral gene expression may occur in some cells, challenging the concept of viral latency. Applying an assay for profiling the transcriptional activity and the chromosomal locations of individual proviruses, we describe a global genomic and epigenetic map of transcriptionally active and silent proviral species and evaluate their longitudinal evolution in persons receiving suppressive ART. Using genome-wide epigenetic reference data, we show that proviral transcriptional activity is associated with activating epigenetic chromatin features in linear proximity of integration sites and in their inter- and intrachromosomal contact regions. Transcriptionally active proviruses were actively selected against during prolonged ART; however, this pattern was violated by large clones of virally infected cells that may outcompete negative selection forces through elevated intrinsic proliferative activity. Our results suggest that transcriptionally active proviruses are dynamically evolving under selection pressure by host factors.