Primates and rodents, which descended from a common ancestor more than 90 million years ago, exhibit profound differences in behavior and cognitive capacity. Modifications, specializations, and innovations to brain cell types may have occurred along each lineage. We used Drop-seq to profile RNA expression in more than 184,000 individual telencephalic interneurons from humans, macaques, marmosets, and mice. Conserved interneuron types varied significantly in abundance and RNA expression between mice and primates, but varied much more modestly among primates. In adult primates, the expression patterns of dozens of genes exhibited spatial expression gradients among neocortical interneurons, suggesting that adult neocortical interneurons are imprinted by their local cortical context. In addition, we found that an interneuron type previously associated with the mouse hippocampus--the "ivy cell", which has neurogliaform characteristics--has become abundant across the neocortex of humans, macaques, and marmosets. The most striking innovation was subcortical: we identified an abundant striatal interneuron type in primates that had no molecularly homologous cell population in mouse striatum, cortex, thalamus, or hippocampus. These interneurons, which expressed a unique combination of transcription factors, receptors, and neuropeptides, including the neuropeptide TAC3, constituted almost 30% of striatal interneurons in marmosets and humans. Understanding how gene and cell-type attributes changed or persisted over the evolutionary divergence of primates and rodents will guide the choice of models for human brain disorders and mutations and help to identify the cellular substrates of expanded cognition in humans and other primates.