We describe an ordering mechanism that arises due to coupling between electronic states at van Hove singularities. This novel mechanism, which naturally leads to ordered structures with small unit cells, couples states near the Fermi energy which are localized at high-symmetry points in k space, in contrast to the conventional mechanism which relies on large parallel sheets of Fermi surface. Using first-principles calculations of the electronic structure of ordered and disordered alloys, we show that this mechanism drives the unusual short- and long-range order found in fcc CuPt.