  We use a geometric generalization of the Seiberg-Witten map between
noncommutative and commutative gauge theories to find the expansion of
noncommutative Chern-Simons (CS) theory in any odd dimension $D$ and at first
order in the noncommutativity parameter $\theta$. This expansion extends the
classical CS theory with higher powers of the curvatures and their derivatives.
  A simple explanation of the equality between noncommutative and commutative
CS actions in $D=1$ and $D=3$ is obtained. The $\theta$ dependent terms are
present for $D\geq 5$ and give a higher derivative theory on commutative space
reducing to classical CS theory for $\theta\to 0$. These terms depend on the
field strength and not on the bare gauge potential.
  In particular, as for the Dirac-Born-Infeld action, these terms vanish in the
slowly varying field strength approximation: in this case noncommutative and
commutative CS actions coincide in any dimension.
  The Seiberg-Witten map on the $D=5$ noncommutative CS theory is explored in
more detail, and we give its second order $\theta$-expansion for any gauge
group. The example of extended $D=5$ CS gravity, where the gauge group is
$SU(2,2)$, is treated explicitly.
