A Note on Noncommutative Chern-Simons Theories

The three dimensional Chern-Simons theory on ${\text{rr}}_{\theta }^2\times \text{rr}$ is studied. Considering the gauge transformations under the group elements which are going to one at infinity, we show that under arbitrary (finite) gauge transformations action changes with an integer multiple of $2\pi$ {\it if}, the level of noncommutaitive Chern-Simons is {\it quantized}. We also briefly discuss the case of the noncommutaitve torus and some other possible extensions.