  Using the Algebraic Bethe Ansatz we consider the correlation functions of the
integrable higher spin chains. We apply a method recently developed for the
spin $\frac 12$ Heisenberg chain, based on the solution of the quantum inverse
problem. We construct a representation for the correlation functions on a
finite chain for arbitrary spin. Then we show how the string solutions of the
Bethe equations can be considered in the framework of this approach in the
thermodynamic limit. Finally, a multiple integral representation for the spin 1
zero temperature correlation functions is obtained in the thermodynamic limit.
