  In a recent breakthrough Kanzieper showed that it is possible to obtain exact
nonperturbative Random Matrix results from the replica limit of the
corresponding Painlev\'e equation. In this article we analyze the replica limit
of the Toda lattice equation and obtain exact expressions for the resolvent of
the chiral Unitary Ensemble both in the quenched limit and in the presence of
additional massive flavors. This derivation explains in a natural way the
appearance of both compact and noncompact integrals, the hallmark of the
supersymmetric method, in the replica limit of the expression for the
resolvent. We also show that the supersymmetric partition function and the
partition function with fermionic replicas are related through the Toda lattice
equation.
