The non-thermal supernova remnant RX J1713.7-3946 (G347.3-0.5) has recently been shown to be a site of cosmic ray (CR) electron acceleration to TeV energies (Muraishi et al. 2000). Here we present evidence that this remnant is also accelerating CR nuclei. Such nuclei can interact with ambient interstellar gas to produce high energy gamma-rays via the decay of neutral pions. We associate the unidentified EGRET GeV gamma- ray source 3EG J1714-3857 with a massive (~3*10 5 Mo) and dense (~500 nucleons cm -3) molecular cloud interacting with RX J1713.7-3946. Direct evidence for such interaction is provided by observations of the lowest two rotational transitions of CO in the cloud; as in other clear cases of interaction, the CO(J=2-1)/CO(J=1-0) ratio is significantly enhanced. Since the cloud is of low radio and X-ray brightness, CR electrons cannot be responsible for the bulk of its GeV emission there. A picture thus emerges where both electrons and nuclei are being accelerated by the SNR: whereas the CR electrons dominate the local non-thermal radio, X-ray and TeV emission, the shock accelerated CR protons and ions (hadrons) are revealed through their interactions in the adjacent massive cloud. Such a scenario had been anticipated by Aharonian, Drury and Volk (1994). ; Comment: 15 pages, 2 low-resolution figures, submitted to ApJL Aug 10, 2001; this version includes referee's suggestions