  In this paper a hithertho unknown symmetry of the three-state chiral Potts
model is found consisting of two coupled Temperley-Lieb algebras. From these we
can construct new superintegrable models. One realisation is in terms of a
staggered isotropic XY spin chain. Further we investigate the importance of the
algebra for the existence of mutually commuting charges. This leads us to a
natural generalisation of the boost-operator, which generates the charges.
