  The possibility that the Galactic dark matter is composed of neutralinos that
are just above half the $Z^o$ mass is examined, in the context of the Galactic
positron excess. In particular, we check if the anomalous bump in the cosmic
ray positron to electron ratio at $10~GeV$ can be explained with the ``decay''
of virtual $Z^o$ bosons produced when the neutralinos annihilate. We find that
the low energy behaviour of our prediction fits well the existing data.
Assuming the neutralinos annihilate primarily in the distant density
concentration in the Galaxy and allowing combination of older, diffused
positrons with young free-streaming ones, produces a fit which is not
satisfactory on its own but is significantly better than the one obtained with
homogeneous injection.
