  A U(N) Chern-Simons theory on noncommutative $\mathbb{R}^{3}$ is constructed
as a $\q$-deformed field theory. The model is characterized by two symmetries:
the BRST-symmetry and the topological linear vector supersymmetry. It is shown
that the theory is finite and $\q_{\m\n}$-independent at the one loop level and
that the calculations respect the restriction of the topological supersymmetry.
Thus the topological $\q$-deformed Chern-Simons theory is an example of a model
which is non-singular in the limit $\q \to 0$.
