A four-mode model of convection in a rotating fluid layer is studied. The model is an extension of the Lorenz model of Rayleigh-B6nard convection, the extra mode accounting for the regeneration of vortieity by rotation. Perturbation theory is applied to show that the Hopf bifurcations from conductive and steady convective solutions can be either supercritical or subcritical. Perturbation theory is also used at large Rayleigh numbers r to predict novel behavior. Supercritical oscillatory convection of finite amplitude is found by numerical integration of the governing equations. The general picture is of a series of oscillatory solutions stable over large r intervals, interspersed by short bursts of chaos.