Cellular progenitors remain poorly characterized in many adult tissues, limited in part by the lack of unbiased techniques to identify progenitors and their progeny. To address this fundamental problem, we developed a novel DNA analog-based lineage-tracing technique to detect multiple rounds of cell division in vivo. Here, we apply this technique to determine the adult lineage mechanism of the insulin-secreting beta cells of pancreatic islets, an important unresolved question in diabetes research. As expected, gastrointestinal and skin epithelia involve specialized progenitors that repeatedly divide to give rise to postmitotic cells. In contrast, specialized progenitors do not contribute to adult beta cells, not even during acute beta cell regeneration. Instead, beta cells are the products of uniform self-renewal, slowed by a replication refractory period that prevents beta cells from immediately redividing. Our approach provides unbiased resolution of previously inaccessible developmental niches and can elucidate lineage mechanisms without candidate markers.