Transcriptional regulatory changes have been shown to contribute to phenotypic differences between species, but many questions remain about how gene expression evolves. Here we report the first comparative study of nascent transcription in primates. We used PRO-seq to map actively transcribing RNA polymerases in resting and activated CD4+ T-cells in multiple human, chimpanzee, and rhesus macaque individuals, with rodents as outgroups. This approach allowed us to directly measure active transcription separately from post-transcriptional processes. We observed general conservation in coding and non-coding transcription, punctuated by numerous differences between species, particularly at distal enhancers and non-coding RNAs. Transcription factor binding sites are a primary determinant of transcriptional differences between species. We found evidence for stabilizing selection on gene expression levels and adaptive substitutions associated with lineage-specific transcription. Finally, rates of evolutionary change are strongly correlated with long-range chromatin interactions. These observations clarify the role of primary transcription in regulatory evolution.