  We consider the nonlinear Schr\"odinger equation on a compact manifold near
an elliptic periodic geodesic. Using a geometric optics construction, we
construct quasimodes to a nonlinear stationary problem which are highly
localized near the periodic geodesic. We show the nonlinear Schr\"odinger
evolution of such a quasimode remains localized near the geodesic, at least for
short times.
