  We give a very simple proof that the renormalization of the Chern-Simons
coupling in the Wilsonian effective action is exhausted at one-loop. Our proof
can apply to arbitrary 2+1-dimensional abelian as well as nonabelian gauge
theories without a bare Chern-Simons coupling, including any non-renormalizable
interactions and non-minimal couplings. Our proof reveals that small (but not
large) gauge invariance is enough to ensure the absence of higher order
corrections.
