Spatial reorientation by layout geometry occurs in numerous species, but its underlying mechanisms are debated. While some argue that navigating animals' sense of place is based on geometric computations over three-dimensional representations, others claim it depends on panoramic image-matching processes. Because children reorient by subtle three-dimensional perturbations of the terrain and not by salient two-dimensional brightness contours on surfaces or freestanding columns, children's sense of place cannot be explained by image matching. To test image-matching theories in a different species, the present experiment investigates the reorientation performance of domestic chicks (Gallus gallus) in environments similar to those used with children. Chicks, like children, spontaneously reoriented by geometric relationships of subtle three-dimensional terrains, and not by salient two-dimensional brightness contours on surfaces or columns. These findings add to the evidence for homologous navigation systems in humans and other vertebrates, and they cast doubt on image-matching theories of reorientation in these species.