We report the first observation of stimulated emission of terahertz radiation from internal transitions of excitons. The far-infrared electromagnetic response of Cu2O is monitored via broadband terahertz pulses after ultrafast resonant excitation of three-dimensional 3p excitons. Stimulated emission from the 3p to the energetically lower 2s bound level occurs at a photon energy of 6.6 meV, with a cross section of ∼10-14  cm2. Simultaneous excitation of both exciton levels, in turn, drives quantum beats, which lead to efficient terahertz emission sharply peaked at the difference frequency.