  We introduce a new family of gauge invariant regularizations of Chern-Simons
theories which generate one-loop renormalizations of the coupling constant of
the form $k\to k+2 s c_v$ where $s$ can take any arbitrary integer value. In
the particular case $s=0$ we get an explicit example of a gauge invariant
regularization which does not generate radiative corrections to the bare
coupling constant. This ambiguity in the radiative corrections to $k$ is
reminiscent of the Coste-L\"uscher results for the parity anomaly in (2+1)
fermionic effective actions.
