Cell-to-cell variation is a universal feature of life that affects a wide range of biological phenomena, from developmental plasticity(1,2) to tumour heterogeneity(3). Although recent advances have improved our ability to document cellular phenotypic variation(4-8), the fundamental mechanisms that generate variability from identical DNA sequences remain elusive. Here we reveal the landscape and principles of mammalian DNA regulatory variation by developing a robust method for mapping the accessible genome of individual cells by assay for transposase-accessible chromatin using sequencing (ATAC-seq)(9) integrated into a programmable microfluidics platform. Single-cell ATAC-seq (scATAC-seq) maps from hundreds of single cells in aggregate closely resemble accessibility profiles from tens of millions of cells and provide insights into cell-to-cell variation. Accessibility variance is systematically associated with specific trans-factors and cis-elements, and we discover combinations of trans-factors associated with either induction or suppression of cell-to-cell variability. We further identify sets of trans-factors associated with cell-type-specific accessibility variance across eight cell types. Targeted perturbations of cell cycle or transcription factor signalling evoke stimulus-specific changes in this observed variability. The pattern of accessibility variation in cis across the genome recapitulates chromosome compartments(10) de novo, linking single-cell accessibility variation to three-dimensional genome organization. Single-cell analysis of DNA accessibility provides new insight into cellular variation of the 'regulome'.