With the capacity for rapid self-renewal and regeneration, the intestinal epithelium is stereotypical of stem cell-supported tissues. Yet the pattern of stem cell turnover remains in question. Applying analytical methods from population dynamics and statistical physics to an inducible genetic labeling system, we showed that clone size distributions conform to a distinctive scaling behavior at short times. This result demonstrates that intestinal stem cells form an equipotent population in which the loss of a stem cell is compensated by the multiplication of a neighbor, leading to neutral drift dynamics in which clones expand and contract at random until they either take over the crypt or they are lost. Combined with long-term clonal fate data, we show that the rate of stem cell replacement is comparable to the cell division rate, implying that neutral drift and symmetrical cell divisions are central to stem cell homeostasis.