  I investigate the effects of the Chern-Simons coupling on high-energy
behavior in $2+1$ dimensional U(1) gauged $\eta(\phi^\dagger\phi)^3$ theory
with a Chern-Simons term. The effective potential and the $\beta$ function for
$\eta$ are calculated to the next-to-leading order of the $1/N$ expansion as
functions of $\theta$ (the Chern-Simons coupling). For all $\theta$, the theory
is found to be driven to instability region at high momenta. It is briefly
discussed on radiative corrections to $\theta$.
