The cerebral cortex has expanded in size and complexity in primates, yet the molecular innovations that enabled primate-specific brain attributes remain obscure. We generated cerebral cortex organoids from human, chimpanzee, orangutan, and rhesus pluripotent stem cells and sequenced their transcriptomes at weekly time points for comparative analysis. We used transcript structure and expression conservation to discover gene regulatory long non-coding RNAs (lncRNAs). Of 2,975 human, multi-exonic lncRNAs, 2,472 were structurally conserved in at least one other species and 920 were conserved in all. Three hundred eighty-six human lncRNAs were transiently expressed (TrEx) and many were also TrEx in great apes (46%) and rhesus (31%). Many TrEx lncRNAs are expressed in specific cell types by single-cell RNA sequencing. Four TrEx lncRNAs selected based on cell-type specificity, gene structure, and expression pattern conservation were ectopically expressed in HEK293 cells by CRISPRa. All induced trans gene expression changes were consistent with neural gene regulatory activity.