  The Darboux transformation applied recurrently on a Schroedinger operator
generates what is called a {\em dressing chain}, or from a different point of
view, a set of supersymmetric shape invariant potentials. The finite-gap
potential theory is a special case of the chain. For the finite-gap case, the
equations of the chain can be expressed as a time evolution of a Hamiltonian
system. We apply Sklyanin's method of separation of variables to the chain. We
show that the classical equation of the separation of variables is the Baxter
T-Q relation after quantization.
