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The shell-type supernova remnant (SNR) RX J1713.7-3946 (G347.3-0.5) was discovered with ROSAT in X-rays and later claimed as source of TeV γ-rays. This object, together with several other southern hemisphere SNRs, is a prime target for observations with the High Energy Stereoscopic System (H.E.S.S.), a new system of imaging atmospheric Cherenkov telescopes which was completed at the end of 2003 in Namibia and is now in full operation. Here we report on observations of the SNR RX J1713.7-3946 which have been performed during the construction and commissioning of the H.E.S.S. system (data originally published here). We confirm TeV emission from this source and present the first ever γ-ray image of an astronomical object resolved on arc minute scales. This image shows shell morphology similar to that seen in X-rays, however at photon energies some nine orders of magnitude higher. The characteristics of the energy spectrum imply efficient acceleration of charged particles to energies beyond 100 TeV, consistent with current ideas of particle acceleration in young SNR shocks. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]