In the mammalian genome, the clustered protocadherin (cPCDH) locus provides a paradigm for stochastic gene expression with the potential to generate a unique cPCDH combination in every neuron. Here we report a chromatin-based mechanism that emerges during the transition from the naive to the primed states of cell pluripotency and reduces, by orders of magnitude, the combinatorial potential in the human cPCDH locus. This mechanism selectively increases the frequency of stochastic selection of a small subset of cPCDH genes after neuronal differentiation in monolayers, 10-month-old cortical organoids and engrafted cells in the spinal cords of rats. Signs of these frequent selections can be observed in the brain throughout fetal development and disappear after birth, except in conditions of delayed maturation such as Down's syndrome. We therefore propose that a pattern of limited cPCDH-gene expression diversity is maintained while human neurons still retain fetal-like levels of maturation.