The absolute-zero specific energies, and the atomic-scale relaxations, of the (100), (110), and (111) surfaces of ordered Cu3Au were calculated using Finnis-Sinclair many-body potentials. The gold-rich truncations of the (100) and (110) surfaces were found to be energetically favored over the gold-poor truncations. This is in agreement with published low-energy ion scattering studies of Cu3Au. The mixed-composition truncations of these low-index surfaces were each found by the calculation to be buckled, with gold atoms displaced toward the vacuum, as compared to copper atoms. A comparison is made to a low-energy electron diffraction study of gold deposited onto the Cu(100), which also showed the buckling of a mixed copper-gold surface, and to embedded-atom method calculations of the low-index surfaces of Ni3Al, which is isomorphic to ordered Cu3Au.