  Spontaneous CP--violation in the minimal supersymmetric standard model with a
gauge singlet and a cubic superpotential is examined. Although the tree--level
Higgs potential conserves CP, it is shown that with the inclusion of the
one--loop top--quark radiative effects, CP may be broken spontaneously. The
CP--violating minimum requires two neutral $(h_1,h_2)$ and one charged
$(H^\pm)$ Higgs--bosons to be relatively light with $m_{h_1}+m_{h_2}
\stackrel{_<}{_\sim} 100~GeV$ and $m_{H^\pm} \stackrel{_<}{_\sim} 110~GeV$. The
electric dipole moment of the electron is in the observable range of $({1 \over
3}~{\rm to}~3) \times 10^{-27}$e-cm.
