  We compute the contribution to the modulus of the one-loop effective action
in pure non-Abelian Chern-Simons theory in an arbitrary covariant gauge. We
find that the results are dependent on both the gauge parameter ($\alpha$) and
the metric required in the gauge fixing. A contribution arises that has not
been previously encountered; it is of the form $(\alpha / \sqrt{p^2}) \epsilon
_{\mu \lambda \nu} p^\lambda$. This is possible as in three dimensions $\alpha$
is dimensionful. A variant of proper time regularization is used to render
these integrals well behaved (although no divergences occur when the
regularization is turned off at the end of the calculation). Since the original
Lagrangian is unaltered in this approach, no symmetries of the classical theory
are explicitly broken and $\epsilon_{\mu \lambda \nu}$ is handled unambiguously
since the system is three dimensional at all stages of the calculation. The
results are shown to be consistent with the so-called Nielsen identities which
predict the explicit gauge parameter dependence using an extension of BRS
symmetry. We demonstrate that this $\alpha$ dependence may potentially
contribute to the vacuum expectation values of products of Wilson loops.
