Understanding the molecular basis for phenotypic differences between humans and other primates remains an outstanding challenge. Mutations in non-coding regulatory DNA that alter gene expression have been hypothesized as a key driver of these phenotypic differences. This has been supported by differential gene expression analyses in general, but not by the identification of specific regulatory elements responsible for changes in transcription and phenotype. To identify the genetic source of regulatory differences, we mapped DNaseI hypersensitive (DHS) sites, which mark all types of active gene regulatory elements, genome-wide in the same cell type isolated from human, chimpanzee, and macaque. Most DHS sites were conserved among all three species, as expected based on their central role in regulating transcription. However, we found evidence that several hundred DHS sites were gained or lost on the lineages leading to modern human and chimpanzee. Species-specific DHS site gains are enriched near differentially expressed genes, are positively correlated with increased transcription, show evidence of branch-specific positive selection, and overlap with active chromatin marks. Species-specific sequence differences in transcription factor motifs found within these DHS sites are linked with species-specific changes in chromatin accessibility. Together, these indicate that the regulatory elements identified here are genetic contributors to transcriptional and phenotypic differences among primate species.