CoPt or FePt equiatomic alloys order according to the tetragonal L10 structure which favors their strong magnetic anisotropy. Conversely magnetism can influence chemical ordering. We present here {\it ab initio} calculations of the stability of the L10 and L12 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.