The outer limit of the Solar System is often considered to be at the distance from the Sun where the solar wind changes from supersonic to subsonic flow. Theory predicts that a termination shock marks this boundary, with locations ranging from a few to over 100 au (1 Au approximately 1.5 x 10(8) km, the distance from Earth to the Sun). 'Pick-up ions' that originate as interstellar neutral atoms should be accelerated to tens of MeV at the termination shock, generating anomalous cosmic rays. Here we report a large increase in the intensity of energetic particles in the outer heliosphere, as measured by an instrument on the Voyager 1 spacecraft. We argue that the spacecraft exited the supersonic solar wind and passed into the subsonic region (possibly beyond the termination shock) on about 1 August 2002 at a distance of approximately 85 Au (heliolatitude approximately 34 degrees N), then re-entered the supersonic solar wind about 200 days later at approximately 87 au from the Sun. We show that the composition of the ions accelerated at the putative termination shock is that of anomalous cosmic rays and of interstellar pick-up ions.