Adult stem cells maintain the mature tissues of metazoans. They do so by reproducing in such a way that their progeny either differentiate, and thus contribute functionally to a tissue, or remain uncommitted and replenish the stem cell pool. Because ageing manifests as a general decline in tissue function, diminished stem cell-mediated tissue maintenance may contribute to age-related pathologies. Accordingly, the mechanisms by which stem cell regenerative potential is sustained, and the extent to which these mechanisms fail with age, are fundamental determinants of tissue ageing. Here, we explore the mechanisms of asymmetric division that account for the sustained fitness of adult stem cells and the tissues that comprise them. In particular, we summarize the theory and experimental evidence underlying non-random chromosome segregation-a mitotic asymmetry arising from the unequal partitioning of chromosomes according to the age of their template DNA strands. Additionally, we consider the possible consequences of non-random chromosome segregation, especially as they relate to both replicative and chronological ageing in stem cells. While biased segregation of chromosomes may sustain stem cell replicative potential by compartmentalizing the errors derived from DNA synthesis, it might also contribute to the accrual of replication-independent DNA damage in stem cells and thus hasten chronological ageing.