Nucleosome positioning is critical to chromatin accessibility and is associated with gene expression programs in cells(1-3). Previous nucleosome mapping methods assemble profiles from cell populations and reveal a cell-averaged pattern: nucleosomes are positioned and form a phased array that surrounds the transcription start sites of active genes(3-6) and DNase I hypersensitive sites(7). However, even in a homogenous population of cells, cells exhibit heterogeneity in expression in response to active signalling(8,9) that may be related to heterogeneity in chromatin accessibility(10-12). Here we report a technique, termed single-cell micrococcal nuclease sequencing (scMNase-seq), that can be used to simultaneously measure genome-wide nucleosome positioning and chromatin accessibility in single cells. Application of scMNase-seq to NIH3T3 cells, mouse primary naive CD4 T cells and mouse embryonic stem cells reveals two principles of nucleosome organization: first, nucleosomes in heterochromatin regions, or that surround the transcription start sites of silent genes, show large variation in positioning across different cells but are highly uniformly spaced along the nucleosome array; and second, nucleosomes that surround the transcription start sites of active genes and DNase I hypersensitive sites show little variation in positioning across different cells but are relatively heterogeneously spaced along the nucleosome array. We found a bimodal distribution of nucleosome spacing at DNase I hypersensitive sites, which corresponds to inaccessible and accessible states and is associated with nucleosome variation and variation in accessibility across cells. Nucleosome variation is smaller within single cells than across cells, and smaller within the same cell type than across cell types. A large fraction of naive CD4 T cells and mouse embryonic stem cells shows depleted nucleosome occupancy at the de novo enhancers detected in their respective differentiated lineages, revealing the existence of cells primed for differentiation to specific lineages in undifferentiated cell populations.