  In this paper, we prove that a Thue equation F(x,y) = h, where h is an
integer and F is a polynomial of degree n with integer coefficients and without
repeated roots, has at most 2n^3 - 2n - 3 solutions provided that the
Mordell-Weil rank of the Jacboian of the corresponding curve is less than
(n-1)(n-2)/2. The proof uses the method of Coleman-Chabauty, extended here to
apply to arbitrary regular models of curves, along with an explicit
construction of a portion of a regular model for the curve corresponding to the
Thue equation.
