  We introduce three universality classes of chiral random matrix ensembles
with a nonzero chemical potential and real, complex or quaternion real matrix
elements. In the thermodynamic limit we find that the distribution of the
eigenvalues in the complex plane does not depend on the Dyson index, and is
given by the solution proposed by Stephanov. For a finite number of degrees of
freedom, $N$, we find an accumulation of eigenvalues on the imaginary axis for
real matrices, whereas for quaternion real matrices we find a depletion of
eigenvalues in this domain. This effect is of order $1/\sqrt N$. In particular
for the real case the resolvent shows a discontinuity of order $1/\sqrt N$.
These results are in agreement with lattice QCD simulations with staggered
fermions and recent instanton liquid simulations both for two colors and
nonzero chemical potential.
