Three-dimensional physical interactions within chromosomes dynamically regulate gene expression in a tissue-specific manner. However, the 3D organization of chromosomes during human brain development and its role in regulating gene networks dysregulated in neurodevelopmental disorders, such as autism or schizophrenia, are unknown. Here we generate high-resolution 3D maps of chromatin contacts during human corticogenesis, permitting large-scale annotation of previously uncharacterized regulatory relationships relevant to the evolution of human cognition and disease. Our analyses identify hundreds of genes that physically interact with enhancers gained on the human lineage, many of which are under purifying selection and associated with human cognitive function. We integrate chromatin contacts with non-coding variants identified in schizophrenia genome-wide association studies (GWAS), highlighting multiple candidate schizophrenia risk genes and pathways, including transcription factors involved in neurogenesis, and cholinergic signalling molecules, several of which are supported by independent expression quantitative trait loci and gene expression analyses. Genome editing in human neural progenitors suggests that one of these distal schizophrenia GWAS loci regulates FOXG1 expression, supporting its potential role as a schizophrenia risk gene. This work provides a framework for understanding the effect of non-coding regulatory elements on human brain development and the evolution of cognition, and highlights novel mechanisms underlying neuropsychiatric disorders.