Embryos allocate cells to the three germ layers in a spatially ordered sequence. Human embryonic stem cells (hESCs) can generate the three germ layers in culture, however, differentiation is typically heterogeneous and spatially disordered. Here we show that geometric confinement is sufficient to trigger self-organized patterning in hESCs. In response to BMP4, these colonies reproducibly differentiate to an outer trophectoderm-like ring, an inner ectodermal circle and a ring of mesendoderm expressing primitive-streak markers in between. Fates are defined relative to the boundary with a fixed length scale: small colonies correspond to the outer layers of larger ones. Inhibitory signals limit the range of BMP4 signaling to the colony edge and induce a gradient of Activin/Nodal signaling that patterns mesendodermal fates. These results demonstrate that the intrinsic tendency of stem cells to make patterns can be harnessed by controlling colony geometries, and provide a quantitative assay for studying paracrine signaling.