A significant fraction of the energy density of the interstellar medium is in the form of high-energy charged particles (cosmic rays). The origin of these particles remains uncertain. Although it is generally accepted that the only sources capable of supplying the energy required to accelerate the bulk of Galactic cosmic rays are supernova explosions, and even though the mechanism of particle acceleration in expanding supernova remnant (SNR) shocks is thought to be well understood theoretically, unequivocal evidence for the production of high-energy particles in supernova shells has proven remarkably hard to find. Here we report on observations of the SNR RX J1713.7 - 3946 (G347.3 - 0.5), which was discovered by ROSAT in the X-ray spectrum and later claimed as a source of high-energy gamma-rays of TeV energies (1 TeV = 10(12) eV). We present a TeV gamma-ray image of the SNR: the spatially resolved remnant has a shell morphology similar to that seen in X-rays, which demonstrates that very-high-energy particles are accelerated there. The energy spectrum indicates efficient acceleration of charged particles to energies beyond 100 TeV, consistent with current ideas of particle acceleration in young SNR shocks.