The recent identification of shear-induced phases in the isotropic melts of liquid crystal polymers shows that these materials are expected to display original nonlinear behaviors. We have investigated the flow behavior of a nematic sidechain polymer above its isotropic-nematic transition temperature. Nonlinear rheology and birefringence measurements indicate the appearance, above a critical shear rate, of the shear-induced isotropic-nematic phase transition. The rheological behavior of this induced phase is characterized by undamped time-periodic shear stress oscillations. These sustained oscillations are interpreted in terms of a stick-slip mechanism alternating high-friction static state and low-friction kinetic state.