The development of perception and control meth-ods that allow bird-scale flapping-wing robots (a.k.a. ornithopters) to perform autonomously is an under-researched area. This paper presents a fully onboard event-based method for ornithopter robot visual guidance. The method uses event cameras to exploit their fast response and robustness against motion blur in order to feed the ornithopter control loop at high rates (100 Hz). The proposed scheme visually guides the robot using line features extracted in the event image plane and controls the flight by actuating over the horizontal and vertical tail deflections. It has been validated on board a real ornithopter robot with real-time computation in low-cost hardware. The experimental evaluation includes sets of experiments with different maneuvers indoors and outdoors.