Molecular self-assembly presents a `bottom-up' approach to the fabrication of objects specified with nanometre precision. DNA molecular structures and intermolecular interactions are particularly amenable to the design and synthesis of complex molecular objects. We report the design and observation of two-dimensional crystalline forms of DNA that self-assemble from synthetic DNA double-crossover molecules. Intermolecular interactions between the structural units are programmed by the design of `sticky ends' that associate according to Watson-Crick complementarity, enabling us to create specific periodic patterns on the nanometre scale. The patterned crystals have been visualized by atomic force microscopy.