We describe a general approach to designing two-dimensional (2D) protein arrays mediated by noncovalent protein-protein interfaces. Protein homo-oligomers are placed into one of the seventeen 2D layer groups, the degrees of freedom of the lattice are sampled to identify configurations with shape-complementary interacting surfaces, and the interaction energy is minimized using sequence design calculations. We used the method to design proteins that self-assemble into layer groups P 3 2 1, P 4 21 2, and P 6. Projection maps of micrometer-scale arrays, assembled both in vitro and in vivo, are consistent with the design models and display the target layer group symmetry. Such programmable 2D protein lattices should enable new approaches to structure determination, sensing, and nanomaterial engineering.