  The $CP^N$ model in three euclidean dimensions is studied in the presence of
a Chern-Simons term using the $1/N$ expansion. The $\beta$-function for the CS
coefficient $\theta$ is found to be zero to order $1/N$ in the unbroken phase
by an explicit calculation. It is argued to be zero to all orders. Some remarks
on the $\theta$ dependence of the critical exponents are also made.
