The three-dimensional Chern-Simons theory on R-theta(2) x R is studied. Con
sidering the gauge transformations under the group elements which are going
to one at infinity, we show that under arbitrary (finite) gauge transforma
tions action changes with an integer multiple of 2 pi if,the level of nonco
mmutative Chern-Simons is quantized. We also briefly discuss the case of th
e noncommutative torus and some other possible extensions. (C) 2001 Publish
ed by Elsevier Science B.V.