VLF hiss is proposed to result from convective beam amplification of incoherent Cerenkov whistler radiation by the beam of precipitating auroral electrons. The beam amplification mechanism is investigated by using the lowest-order WKB wave kinetic equation and linear growth rates. It is shown that incoherent Cerenkov radiation cannot produce strong VLF hiss without beam amplification and that the beam amplification mechanism can account for the observed bandwidth and power fluxes of strong VLF hiss when the electron gyrofrequency is less than the electron plasma frequency. The theory is not adequate for high frequencies when the electron plasma frequency is less than the electron gyrofrequency, because nonlinear processes are important for frequencies near the plasma frequency.