  We construct a random matrix model that, in the large $N$ limit, reduces to
the low energy limit of the QCD partition function put forward by Leutwyler and
Smilga. This equivalence holds for an arbitrary number of flavors and any value
of the QCD vacuum angle. In this model, moments of the inverse squares of the
eigenvalues of the Dirac operator obey sum rules, which we conjecture to be
universal. In other words, the validity of the sum rules depends only on the
symmetries of the theory but not on its details. To illustrate this point we
show that the sum rules hold for an interacting liquid of instantons. The
physical interpretation is that the way the thermodynamic limit of the spectral
density near zero is approached is universal. However, its value, $i.e.$ the
chiral condensate, is not.
