Tissue homeostasis relies on rewiring of stem cell transcriptional programs into those of differentiated cells. Here, we investigate changes in chromatin occurring in a bipotent adult stem cells. Combining mapping of chromatin-associated factors with statistical modeling, we identify genome-wide transitions during differentiation in the adult Drosophila intestinal stem cell (ISC) lineage. Active, stem-cell-enriched genes transition to a repressive heterochromatin protein-1-enriched state more prominently in enteroendocrine cells (EEs) than in enterocytes (ECs), in which the histone H1-enriched Black state is preeminent. In contrast, terminal differentiation genes associated with metabolic functions follow a common path from a repressive, primed, histone H1-enriched Black state in ISCs to active chromatin states in EE and EC cells. Furthermore, we find that lineage priming has an important function in adult ISCs, and we identify histone H1 as a mediator of this process. These data define underlying principles of chromatin changes during adult multipotent stem cell differentiation.