We report the operation of a Bloch oscillator. The active medium was a staticvoltage driven, doped GaAs/AlAs superlattice which was electromagnetically coupled to a resonator. The oscillator produced tuneable microwave radiation (frequency ~ 60 GHz; power ~ 0.5 mW; efficiency ~ 4 %). The gain (~ 10^4 /cm) was due to the nonlinearity mediated by miniband electrons. We also present a theory of the oscillator. The Bloch oscillator should in principle be feasible for generation of radiation up to frequencies of 10 THz and more.