Past and recent observations indicate the presence of lightning at altitudes in excess of 30 km. The phenomenon is manifested as a high altitude optical flash, correlated with the presence of giant thunderstorms in the atmosphere below. This letter presents the first physical model of the process. The model is based on low frequency RF breakdown of the upper atmosphere, ignited by the upward propagating electromagnetic pulses due to conventional low altitude lightning. Horizontal intercloud lightning strokes form the optimal configuration. Horizontal lightning discharges with cloud-to-cloud moment charge ~6,000--8,000 C-km account for the observed level of optical emissions. ¿ American Geophysical Union 1995