The rapid turnover of the mammalian intestinal epithelium is supported by stem cells located around the base of the crypt. In addition to the Lgr5 marker, intestinal stem cells have been associated with other markers that are expressed heterogeneously within the crypt base region. Previous quantitative clonal fate analyses have led to the proposal that homeostasis occurs as the consequence of neutral competition between dividing stem cells. However, the short-term behaviour of individual Lgr5+ cells positioned at different locations within the crypt base compartment has not been resolved. Here we establish the short-term dynamics of intestinal stem cells using the novel approach of continuous intravital imaging of Lgr5-Confetti mice. We find that Lgr5+ cells in the upper part of the niche (termed `border cells') can be passively displaced into the transit-amplifying domain, after the division of proximate cells, implying that the determination of stem-cell fate can be uncoupled from division. Through quantitative analysis of individual clonal lineages, we show that stem cells at the crypt base, termed `central cells', experience a survival advantage over border stem cells. However, through the transfer of stem cells between the border and central regions, all Lgr5+ cells are endowed with long-term self-renewal potential. These findings establish a novel paradigm for stem-cell maintenance in which a dynamically heterogeneous cell population is able to function long term as a single stem-cell pool.