Protons with energies up to ∼1015 eV are the main component of cosmic rays, but evidence for the specific locations where they could have been accelerated to these energies has been lacking. Electrons are known to be accelerated to cosmic-ray energies in supernova remnants, and the shock waves associated with such remnants, when they hit the surrounding interstellar medium, could also provide the energy to accelerate protons. The signature of such a process would be the decay of pions (π0), which are generated when the protons collide with atoms and molecules in an interstellar cloud: pion decay results in γ-rays with a particular spectral-energy distribution. Here we report the observation of cascade showers of optical photons resulting from γ-rays at energies of ∼1012 eV hitting Earth's upper atmosphere, in the direction of the supernova remnant RX J1713.7-3946. The spectrum is a good match to that predicted by pion decay, and cannot be explained by other mechanisms.