The human brain has changed dramatically since humans diverged from our closest living relatives, chimpanzees and the other great apes. However, the genetic and developmental programs underlying this divergence are not fully understood. Here, we generate single-nucleus RNA-seq data of human, chimpanzee and macaque adult prefrontal cortex. Spatial information is obtained by isolating nuclei from sequential sections sliced from basal to apical positions. By comparing transcriptome of different cell types in the three species, we map human-specific expression in adult prefrontal cortex. By comparing to single cell RNA-seq data of cerebral organoids of the same species, we find developmental differences that persist into adulthood, as well as cell state-specific changes that occur exclusively in the adult brain.