  We derive the free energy of the chiral Potts model by the infinite lattice
``inversion relation'' method. This method is non-rigorous in that it always
needs appropriate analyticity assumptions. Guided by previous calculations
based on exact finite-lattice functional relations, we find that in addition to
the usual assumption that the free energy be analytic and bounded in some
principal domain of the rapidity parameter space that includes the physical
regime, we also need a much less obvious symmetry. We can then obtain the free
energy by Wiener-Hopf factorization in the complex planes of appropriate
variables. Together with the inversion relation, this symmetry relates the
values of the free energy in all neighbouring domains to those in the principal
domain.
