  We study the Yang-Mills-Chern-Simons theory systematically in an effort to
generalize the Coleman-Hill result to the non-Abelian case. We show that, while
the Chern-Simons coefficient is in general gauge dependent in a non-Abelian
theory, it takes on a physical meaning in the axial gauge. Using the
non-Abelian Ward identities as well as the analyticity of the amplitudes in the
momentum variables, we show that, in the axial gauge, the Chern-Simons
coefficient does not receive any quantum correction beyond one loop. This
allows us to deduce that the ratio ${4\pi m\over g^{2}}$ is unrenormalized, in
a non-Abelian theory, beyond one loop in any infrared safe gauge. This is the
appropriate generalization of the Coleman-Hill result to non-Abelian theories.
Various other interesting properties of the theory are also discussed.
