Cellular function in tissue is dependent on the local environment, requiring new methods for spatial mapping of biomolecules and cells in the tissue context1. The emergence of spatial transcriptomics has enabled genome-scale gene expression mapping2-5, but the ability to capture spatial epigenetic information of tissue at the cellular level and genome scale is lacking. Here we describe a method for spatially resolved chromatin accessibility profiling of tissue sections using next-generation sequencing (spatial-ATAC-seq) by combining in situ Tn5 transposition chemistry6 and microfluidic deterministic barcoding5. Profiling mouse embryos using spatial-ATAC-seq delineated tissue-region-specific epigenetic landscapes and identified gene regulators involved in the development of the central nervous system. Mapping the accessible genome in the mouse and human brain revealed the intricate arealization of brain regions. Applying spatial-ATAC-seq to tonsil tissue resolved the spatially distinct organization of immune cell types and states in lymphoid follicles and extrafollicular zones. This technology progresses spatial biology by enabling spatially resolved chromatin accessibility profiling to improve our understanding of cell identity, cell state and cell fate decision in relation to epigenetic underpinnings in development and disease.