Cells differentiate when transcription factors bind accessible cis-regulatory elements to establish specific gene expression programs. In differentiating embryonic stem cells, chromatin at lineage-restricted genes becomes sequentially accessible, probably by means of 'pioneer' transcription factor activity, but tissues may use other strategies in vivo. Lateral inhibition is a pervasive process in which one cell forces a different identity on its neighbours, and it is unclear how chromatin in equipotent progenitors undergoing lateral inhibition quickly enables distinct, transiently reversible cell fates. Here we report the chromatin and transcriptional underpinnings of differentiation in mouse small intestine crypts, where notch signalling mediates lateral inhibition to assign progenitor cells into absorptive or secretory lineages. Transcript profiles in isolated LGR5(+) intestinal stem cells and secretory and absorptive progenitors indicated that each cell population was distinct and the progenitors specified. Nevertheless, secretory and absorptive progenitors showed comparable levels of H3K4me2 and H3K27ac histone marks and DNase I hypersensitivity--signifying accessible, permissive chromatin-at most of the same cis-elements. Enhancers acting uniquely in progenitors were well demarcated in LGR5(+) intestinal stem cells, revealing early priming of chromatin for divergent transcriptional programs, and retained active marks well after lineages were specified. On this chromatin background, ATOH1, a secretory-specific transcription factor, controls lateral inhibition through delta-like notch ligand genes and also drives the expression of numerous secretory lineage genes. Depletion of ATOH1 from specified secretory cells converted them into functional enterocytes, indicating prolonged responsiveness of marked enhancers to the presence or absence of a key transcription factor. Thus, lateral inhibition and intestinal crypt lineage plasticity involve interaction of a lineage-restricted transcription factor with broadly permissive chromatin established in multipotent stem cells.