  By computing the two-loop effective potential of the D=3 N=1 supersymmetric
Chern-Simons model minimally coupled to a massless self-interacting matter
superfield, it is shown that supersymmetry is preserved, while the internal
U(1) and the scale symmetries are broken at two-loop order, dynamically
generating masses both for the gauge superfield and for the real component of
the matter superfield.
