  We present non-trivial interactions of N=1 self-dual massive vector multiplet
in three-dimensions, with gauged scale covariance. Our multiplets are a vector
multiplet (A_\mu, \lambda) and a gauge multiplet (B_\mu, \chi), where the
latter is used for the gauging of the scale covariance of the former. Due tothe
absence of supergravity, this system has no lagrangian formulation, but has
only a set of field equations. The gauge multiplet can also have
Dirac-Born-Infeld type interactions, even in the presence of the massive
self-dual vector multiplet. As a by-product, we also show that scale covariant
couplings are possible for scalar multiplet. We also try a mechanism of
spontaneous breaking of scale covariance by introducing a superpotential for
scalar multiplets.
