  We study baryogenesis at the electroweak phase transition of the universe
within the framework of the supersymmetric standard model (SSM) based on N=1
supergravity. This model contains a new source of CP violation in the
mass-squared matrices for squarks, which could enable $t$ squarks to mediate
the charge transport mechanism for generating baryon asymmetry. The same
CP-violating source also induces the electric dipole moment (EDM) of the
neutron at the one-loop level. If the new CP-violating phase is not suppressed,
it is shown, the $t$-squark transport can lead to baryon asymmetry consistent
with its observed value within reasonable ranges of SSM parameters. For these
parameter ranges the magnitude of the neutron EDM is predicted to be not much
smaller than its present experimental upper bound.
