  We analyze the singlet $P$--wave charmonium production at $e^+ e^-$ colliders
within the framework of unconstrained supersymmetry. We show that the
CP--violating transitions, dominated by the gluino exchange, are typically four
orders of magnitude larger than the CP--conserving ones, and former is
generated by the electric dipole moment of the charm quark. Our results can be
directly tested via the charmonium searches at the CLEO--c experiment.
