Owing to surface diffusion, the molecular beam epitaxy (MBE) technique has made it possible to produce new binary alloy films by coevaporation on a single-crystal substrate in an ultrahigh vacuum. In this fashion, a hexagonal close-packed (hcp) structure of the Co 3 Pt compound with ferromagnetic and chemical order has been discovered recently which was not previously known in the bulk alloy equilibrium phase diagram. Using a tight-binding linear muffin-tin orbital (TB-LMTO) method for the electronic structure of Co 3 Pt, we treat first the reference case of the fcc L1 2 phase and then the hcp phase. In this last phase we consider both the standard DO 19 structure and a modified version of it. We perform the band-structure calculation in both the paramagnetic and ferromagnetic cases, and on the basis of a total energy calculation we arrive at the conclusion that the ferromagnetic phase of the DO 19 structure is the most stable.