  The severity of the sign problem in lattice QCD at nonzero baryon density is
measured by the average phase of the fermion determinant. Motivated by the
equivalence of chiral random matrix theory and QCD to leading order in the
epsilon regime, we compute the phase of the fermion determinant for general
topology in random matrix theory as a function of the quark chemical potential
and the quark mass. We find that the sign problem becomes milder with
increasing topological charge. The analytic predictions are verified by
detailed numerical random matrix simulations.
