SS 433 is a binary system containing a supergiant star that is overflowing its Roche lobe with matter accreting onto a compact object (either a black hole or neutron star)(1-3). Two jets of ionized matter with a bulk velocity of approximately 0.26c (where c is the speed of light in vacuum) extend from the binary, perpendicular to the line of sight, and terminate inside W50, a supernova remnant that is being distorted by the jets(2,4-8). SS 433 differs from other microquasars (small-scale versions of quasars that are present within our own Galaxy) in that the accretion is believed to be super-Eddington(9-11), and the luminosity of the system is about 10(40) ergs per second(2,9,12,13). The lobes of W50 in which the jets terminate, about 40 parsecs from the central source, are expected to accelerate charged particles, and indeed radio and X-ray emission consistent with electron synchrotron emission in a magnetic field have been observed(14-16). At higher energies (greater than 100 gigaelectronvolts), the particle fluxes of.-rays from X-ray hotspots around SS 433 have been reported as flux upper limits(6,17-20). In this energy regime, it has been unclear whether the emission is dominated by electrons that are interacting with photons from the cosmic microwave background through inverse-Compton scattering or by protons that are interacting with the ambient gas. Here we report teraelectronvolt gamma-ray observations of the SS 433/W50 system that spatially resolve the lobes. The teraelectronvolt emission is localized to structures in the lobes, far from the centre of the system where the jets are formed. We have measured photon energies of at least 25 teraelectronvolts, and these are certainly not Doppler-boosted, because of the viewing geometry. We conclude that the emission-from radio to teraelectronvolt energies-is consistent with a single population of electrons with energies extending to at least hundreds of teraelectronvolts in a magnetic field of about 16 microgauss.