We describe a lattice of InAs nanowires that spontaneously organizes in three dimensions within an InAs/GaSb superlattice grown under high As4 flux. As characterized by x-ray diffraction and cross-sectional scanning tunneling microscopy, the periodic nanowires are ∼10 nm high, 120 nm wide, and many microns long along [110], with face-centered cubic-like vertical ordering within the superlattice. The unusual vertical ordering creates a lateral composition modulation with half the period of the nanowires. The structure appears to arise from the InAs misfit stress combined with specific InAs and GaSb growth kinetic effects.