  A new link invariant is derived using the exactly solvable chiral Potts model
and a generalized Gaussian summation identity. Starting from a general
formulation of link invariants using edge-interaction spin models, we establish
the uniqueness of the invariant for self-dual models. We next apply the
formulation to the self-dual chiral Potts model, and obtain a link invariant in
the form of a lattice sum defined by a matrix associated with the link diagram.
A generalized Gaussian summation identity is then used to carry out this
lattice sum, enabling us to cast the invariant into a tractable form. The
resulting expression for the link invariant is characterized by roots of unity
and does not appear to belong to the usual quantum group family of invariants.
A table of invariants for links with up to 8 crossings is given.
