For the integrable chiral Potts model, the weights are defined by a high genus curve, the chiral Potts curve. Unlike the other solvable models, whose weights are parametrized by curves of genus less or equal to one, so that they can be expressed in terms of trigonometric functions, rational functions for the genus zero case, or by theta functions for the genus 1 case, this model involves high genus theta functions, for which the theory is less well-developed.