We report the detection of pulsed gamma rays from the Crab pulsar at energies above 100 giga–electron volts (GeV) with the Very Energetic Radiation Imaging Telescope Array System (VERITAS) array of atmospheric Cherenkov telescopes. The detection cannot be explained on the basis of current pulsar models. The photon spectrum of pulsed emission between 100 mega–electron volts and 400 GeV is described by a broken power law that is statistically preferred over a power law with an exponential cutoff. It is unlikely that the observation can be explained by invoking curvature radiation as the origin of the observed gamma rays above 100 GeV. Our findings require that these gamma rays be produced more than 10 stellar radii from the neutron star.