We live in a macroscopic three-dimensional (3D) world, but our best description of the structure of matter is at the atomic and molecular scale. Understanding the relationship between the two scales requires a bridge from the molecular world to the macroscopic world. Connecting these two domains with atomic precision is a central goal of the natural sciences, but it requires high spatial control of the 3D structure of matter. The simplest practical route to producing precisely designed 3D macroscopic objects is to form a crystalline arrangement by self-assembly, because such a periodic array has only conceptually simple requirements: a motif that has a robust 3D structure, dominant affinity interactions between parts of the motif when it self-associates, and predictable structures for these affinity interactions. Fulfilling these three criteria to produce a 3D periodic system is not easy, but should readily be achieved with well-structured branched DNA motifs tailed by sticky ends. Complementary sticky ends associate with each other preferentially and assume the well-known B-DNA structure when they do so; the helically repeating nature of DNA facilitates the construction of a periodic array. It is essential that the directions of propagation associated with the sticky ends do not share the same plane, but extend to form a 3D arrangement of matter. Here we report the crystal structure at 4Å resolution of a designed, self-assembled, 3D crystal based on the DNA tensegrity triangle. The data demonstrate clearly that it is possible to design and self-assemble a well-ordered macromolecular 3D crystalline lattice with precise control.