The self-assembly of colloidal particles into the cubic diamond structure has been a longstanding goal because of its potential for making materials with a photonic band gap. These materials suppress the spontaneous emission of light and are valued for their applications as optical waveguides, filters, laser resonators, for improving light-harvesting technologies, and for other applications. Here we describe and demonstrate a method for making colloidal particles that self-assemble into cubic colloidal diamond. The particles consist of partially compressed tetrahedral clusters with retracted sticky patches. They self-assemble via patch-patch adhesion in coordination with a steric interlock mechanism that selects the proper staggered bond conformation required for cubic diamond. The combination of particle shape and patchy interactions make it possible to self-assemble structures not realized previously.