  The expectation value of the complex phase factor of the fermion determinant
is computed in the microscopic domain of QCD at nonzero chemical potential. We
find that the average phase factor is non-vanishing below a critical value of
the chemical potential equal to the half the pion mass and vanishes
exponentially in the volume for larger values of the chemical potential. This
holds for QCD with dynamical quarks as well as for quenched and phase quenched
QCD. The average phase factor has an essential singularity for zero chemical
potential and cannot be obtained by analytic continuation from imaginary
chemical potential or by means of a Taylor expansion. The leading order
correction in the $p$-expansion of the chiral Lagrangian is calculated as well.
