  We study the spectrum of the QCD Dirac operator near zero virtuality for $N_c
=2$. According to a universality argument, it can be described by a random
matrix theory with the chiral structure of QCD, but with $real$ matrix
elements. Using results derived by Mehta and Mahoux and Nagao and Wadati, we
are able to obtain an analytical result for the microscopic spectral density
that in turn is the generating function for Leutwyler-Smilga type spectral sum
rules.
