We present a new instability observed in rapid granular flows down rough inclined planes. For high inclinations and flow rates, the free surface of the flow experiences a regular deformation in the transverse direction. Measurements of the surface velocities imply that this instability is associated with the formation of longitudinal vortices in the granular flow. From the experimental observations, we propose a mechanism for the longitudinal vortex formation based on the concept of granular temperature.