  In this talk we present the results published recently in Ref. [1], where we
showed how to introduce a quark chemical potential in the overlap Dirac
operator. The resulting operator satisfies a Ginsparg-Wilson relation and has
exact zero modes. It is no longer gamma_5-Hermitian, but its nonreal
eigenvalues still occur in pairs. We compute the spectral density of the
operator on the lattice and show that, for small eigenvalues, the data agree
with analytical predictions of non-Hermitian chiral random matrix theory for
both trivial and nontrivial topology. We also explain an observed change in the
number of zero modes as a function of chemical potential.
