Chern-Simons Theories on Noncommutative Plane

We investigate U(N) Chern-Simons theories on noncommutative plane. We show that for the theories to be consistent quantum mechanically, the coefficient of the Chern-Simons term should be quantized $\kappa =n\mathrm{/}2\pi$ with an integer $n$. This is a surprise for the U(1) gauge theory. When uniform background charge density ${\rho }_e$ is present, the quantization rule changes to $\kappa +\rho_e\theta = n/2\pi$withnoncommutativeparameter$\theta$. With the exact expression for the angular momentum, we argue in the U(1) theory that charged particles in the symmetric phase carry fractional spin $1\mathrm{/}2n$ and vortices in the broken phase carry half-integer or integer spin $-n\mathrm{/}2$.