CoPt equiatomic alloy orders according to the tetragonal L1(0) structure which favors strong magnetic anisotropy. Conversely, magnetism can influence the chemical ordering. We present here ab initio calculations of the stability of the L1(0) and L1(2) structures of Co-Pt alloys in their paramagnetic and ferromagnetic states. They show that magnetism strongly reinforces the ordering tendencies in this system. A simple tight-binding analysis allows us to account for this behavior in terms of some pertinent parameters.