  Abelian Chern-Simons gauge theory is known to possess a `$S$-self-dual'
action where its coupling constant $k$ is inverted {\it i.e.} $k
\leftrightarrow {1 \over k}$. Here a vector non-abelian duality is found in the
pure non-abelian Chern-Simons action at the classical level. The dimensional
reduction of the dual Chern-Simons action to two-dimensions constitutes a dual
Wess-Zumino-Witten action already given in the literature.
