  We consider the noncommutative extension of Chern-Simons theory. We show the
the theory can be fully expanded in power series of the noncommutative
parameter theta and that no non-analytical sector exists. The theory appears to
be unstable under radiative corrections, but we show that the infinite set of
instabilities, to all orders in \hbar and in theta, is confined to a BRS exact
cocycle. We show also that the theory is anomaly free. The quantum theory
cannot be written in terms of the Groenewald-Moyal star product, and hence
doubts arise on the interpretation of the noncommutative nature of the
underlying spacetime. Nonetheless, the deformed theory is well defined as a
quantum field theory, and the beta function of the Chern-Simons coupling
constant vanishes, as in the ordinary Chern-Simons theory.
