We observe dramatic changes in the near-field and far-field emission from a semiconductor microcavity excited by a pulsed and nonresonant optical pump with varying power. Above a threshold pumping power, light is emitted by a single quantum state lying at the bottom of the lower exciton-polariton band. Its intensity increases exponentially with the pump power and its linewidth becomes narrower than the cavity mode width. Near-field spectroscopy shows that the stimulated emission comes from several bright spots in the cavity plane, but no diffraction-induced angular broadening of the emission is observed. This is direct evidence for spontaneous formation of a nonequilibrium Bose condensate of coherent exciton polaritons with their wave function sharply peaked at structural imperfections.