Pulsar systems accelerate particles to immense energies. The detailed functioning of these engines is still poorly understood, but polarization measurements of high-energy radiation may allow us to locate where the particles are accelerated. We have detected polarized gamma rays from the vicinity of the Crab pulsar using data from the spectrometer on the International Gamma-Ray Astrophysics Laboratory satellite. Our results show polarization with an electric vector aligned with the spin axis of the neutron star, demonstrating that a substantial fraction of the high-energy electrons responsible for the polarized photons are produced in a highly ordered structure close to the pulsar.