The previous theory of high-gain free-electron laser (FEL) operating in the quantum regime is semiclassical because the electron dynamic is quantized but the radiation field is classically described. Here, we present for the first time a fully quantum mechanical theory where also the field is quantized. We shall restrict to the FEL operation in the steady state regime where the slippage length is much smaller than the bunch length. The results predicted by this theory are quite different from those of the semiclassical theory.