There are a few lattice models of interacting systems that can be solved exactly, in the sense that one can calculate the free energy in the thermodynamic limit of a large system. The interesting ones are mostly two-dimensional, such as the Ising model and the six and eight-vertex models. A comparitively recent addition to the list is the chiral Potts model. This is more difficult mathematically than its predecessors. While its free energy was calculated in 1988, until now there has only been a conjecture (a very elegant one) for the order parameters, i.e. the spontaneous magnetizations. This conjecture has now been verified, and in this talk I shall discuss the difficulties encountered and the method used.