Intestinal organoids are complex three-dimensional structures that mimic the cell-type composition and tissue organization of the intestine by recapitulating the self-organizing ability of cell populations derived from a single intestinal stem cell. Crucial in this process is a first symmetry-breaking event, in which only a fraction of identical cells in a symmetrical sphere differentiate into Paneth cells, which generate the stem-cell niche and lead to asymmetric structures such as the crypts and villi. Here we combine single-cell quantitative genomic and imaging approaches to characterize the development of intestinal organoids from single cells. We show that their development follows a regeneration process that is driven by transient activation of the transcriptional regulator YAP1. Cell-to-cell variability in YAP1, emerging in symmetrical spheres, initiates Notch and DLL1 activation, and drives the symmetry-breaking event and formation of the first Paneth cell. Our findings reveal how single cells exposed to a uniform growth-promoting environment have the intrinsic ability to generate emergent, self-organized behaviour that results in the formation of complex multicellular asymmetric structures.