The relation between the Dirac quantization condition of magnetic charge an
d the quantization of the Chern-Simons coefficient is obtained. It implies
that in a (2+1)-dimensional QED with the Chern-Simons topological mass term
and the existence of a magnetic monopole with magnetic charge g, the Chern
-Simons coefficient must also be quantized, just as in the non-Abelian case
.