High-energy cosmic rays (relativistic heavy nuclei) play an important role in heating interstellar matter in the Milky Way(1,2), and they affect chemical abundances through collisions with atoms in the interstellar gas(2). Although it has long been thought that these cosmic rays arise from supernovae(3,4), direct evidence for such an association has been lacking. Here we report X-ray observations of the remnant of supernova 1006, made by the ASCA satellite, which indicate that emission from the edges of the remnant shell is dominated by radiation from electrons accelerated to energies of similar to 100 TeV within the shock front. Ions in the shell are likely to have been accelerated to similar energies, thus giving rise to very-high-energy cosmic rays.