During mammalian development, differences in chromatin state coincide with cellular differentiation and reflect changes in the gene regulatory landscape1. In the developing brain, cell fate specification and topographic identity are important for defining cell identity2 and confer selective vulnerabilities to neurodevelopmental disorders3. Here, to identify cell-type-specific chromatin accessibility patterns in the developing human brain, we used a single-cell assay for transposase accessibility by sequencing (scATAC-seq) in primary tissue samples from the human forebrain. We applied unbiased analyses to identify genomic loci that undergo extensive cell-type- and brain-region-specific changes in accessibility during neurogenesis, and an integrative analysis to predict cell-type-specific candidate regulatory elements. We found that cerebral organoids recapitulate most putative cell-type-specific enhancer accessibility patterns but lack many cell-type-specific open chromatin regions that are found in vivo. Systematic comparison of chromatin accessibility across brain regions revealed unexpected diversity among neural progenitor cells in the cerebral cortex and implicated retinoic acid signalling in the specification of neuronal lineage identity in the prefrontal cortex. Together, our results reveal the important contribution of chromatin state to the emerging patterns of cell type diversity and cell fate specification and provide a blueprint for evaluating the fidelity and robustness of cerebral organoids as a model for cortical development.