  The exact solution is obtained for the eigenvalues and eigenvectors of the
row-to-row transfer matrix of a two-dimensional vertex model with unlimited
number of states per bond. This model is a classical counterpart of a quantum
spin chain with an unlimited value of spin. This quantum chain is studied using
general predictions of conformal field theory. The long-distance behaviour of
some ground-state correlation functions is derived from a finite-size analysis
of the gapless excitations.
