Various nonlinear rotation regimes are observed in an optically excited nematic liquid crystal film under boundary conditions (for the light and the material) that are invariant by rotation. Th excitation light is circularly polarized, the intensity profile is circularly symmetric and the beam diameter at the sample location is a few times smaller than the cell thickness. A transition to chaos via quasiperiodicity is identified when the light intensity is taken as the control parameter. Transverse nonlocal effects are suggested to be the cause of the observed dynamics and a simple model consisting of a collection of coupled rotators is developed to provide a qualitative explanation.