Human glioblastomas harbour a subpopulation of glioblastoma stem cells that drive tumorigenesis. However, the origin of intratumoural functional heterogeneity between glioblastoma cells remains poorly understood. Here we study the clonal evolution of barcoded glioblastoma cells in an unbiased way following serial xenotransplantation to define their individual fate behaviours. Independent of an evolving mutational signature, we show that the growth of glioblastoma clones in vivo is consistent with a remarkably neutral process involving a conserved proliferative hierarchy rooted in glioblastoma stem cells. In this model, slow-cycling stem-like cells give rise to a more rapidly cycling progenitor population with extensive self-maintenance capacity, which in turn generates non-proliferative cells. We also identify rare 'outlier' clones that deviate from these dynamics, and further show that chemotherapy facilitates the expansion of pre-existing drug-resistant glioblastoma stem cells. Finally, we show that functionally distinct glioblastoma stem cells can be separately targeted using epigenetic compounds, suggesting new avenues for glioblastoma-targeted therapy.