Phase of the Fermion Determinant at Nonzero Chemical Potential

We show that in the microscopic domain of QCD (also known as the domain) at nonzero chemical potential the average phase factor of the fermion determinant is nonzero for micro<m(pi)/2 and is exponentially suppressed for larger values of the chemical potential. This follows from the chiral Lagrangian that describes the low-energy limit of the expectation value of the phase factor. Explicit expressions for the average phase factor are derived using a random matrix formulation of the zero momentum limit of this chiral Lagrangian.