  Requiring that the baryon number of the universe be generated by anomalous
electroweak interactions places strong constraints on the minimal
supersymmetric standard model. In particular, the electric dipole moment of the
neutron must be greater than $10^{-27}$e-cm. Improvement of the current
experimental bound on the neutron's electric dipole moment by one order of
magnitude would constrain the lightest chargino to be lighter than 88 GeV, and
the the lightest neutralino to be lighter than 44 GeV. In extensions of this
model with gauge singlet superfields all of these bounds are eliminated.
