We report measurements of mm-wavelength radiation from two-dimensional arrays of underdamped Josephson junctions. All of our samples emit coherently in a novel synchronized state, which is triggered by a resonance in the array structure. Measurements of the detected power as a function of the number N of active junctions show a threshold, suggesting population inversion. Above threshold, the power scales with N-2 up to an array size bigger than the free-space radiation wavelength. The highest measured conversion efficiency from de to ac power is about 17%. Our data are consistent with stimulated emission causing coherence and cannot be explained by existing classical coupling mechanisms.