The idea that stem cells of adult tissues with high turnover are protected from DNA replication-induced mutations by maintaining the same 'immortal' template DNA strands together through successive divisions has been tested in several tissues. In the epithelium of the small intestine, the provided evidence was based on the assumption that stem cells are located above Paneth cells. The results of genetic lineage-tracing experiments point instead to crypt base columnar cells intercalated between Paneth cells as bona fide stem cells. Here we show that these cells segregate most, if not all, of their chromosomes randomly, both in the intact and in the regenerating epithelium. Therefore, the 'immortal' template DNA strand hypothesis does not apply to intestinal epithelial stem cells, which must rely on other strategies to avoid accumulating mutations.