  We analyze an abelian gauge model in 3 dimensions which includes massless
scalar matter fields. By controlling the trace anomalies with a local
dilatation Ward identity, we show that, in perturbation theory and within the
BPHZL scheme, the Chern-Simons term has no radiative corrections. This implies,
in particular, the vanishing of the corresponding $\beta$ function in the
renormalization group equation.
