The Crab Nebula is a bright source of gamma rays powered by the Crab Pulsar's rotational energy through the formation and termination of a relativistic electron-positron wind. We report the detection of gamma rays from this source with energies from 5 x 10(-4) to 1.1 peta-electron volts with a spectrum showing gradual steepening over three energy decades. The ultrahigh-energy photons imply the presence of a peta-electron volt electron accelerator (a pevatron) in the nebula, with an acceleration rate exceeding 15% of the theoretical limit. We constrain the pevatron's size between 0.025 and 0.1 parsecs and the magnetic field to approximate to 110 microgauss. The production rate of peta-electron volt electrons, 2.5 x 10(36) ergs per second, constitutes 0.5% of the pulsar spin-down luminosity, although we cannot exclude a contribution of peta-electron volt protons to the production of the highest-energy gamma rays.