We investigate the spectral properties of a random matrix model which
in the large N limit embodies the essentials of the QCD partition func
tion at low energy. The exact spectral density and its pair correlatio
n function are derived for an arbitrary number of flavors and zero top
ological charge. Their microscopic limits provide the master formulae
for sum rules for the inverse powers of the eigenvalues of the QCD Dir
ac operator, as recently discussed by Leutwyler and Smilga.