We report on the discovery of a diffuse X-ray source with ASCA , presumably associated with a molecular cloud in the vicinity of the supernova remnant RX J1713.7 - 3946 . The energy spectrum ( 1–10 keV ) of the hard X-ray source shows a flat continuum , which is described by a power-law with a photon index of \Gamma = 1.0 ^ { +0.4 } _ { -0.3 } . We argue that this unusually flat spectrum can be best interpreted in terms of characteristic bremsstrahlung emission from the loss-flattened distribution of either sub-relativistic protons or mildly relativistic electrons . The strong shock of RX J1713.7 - 3946 , which is likely to interact with the molecular cloud , as evidenced by CO-line observations , seems to be a natural site of acceleration of such nonthermal particles . The observed luminosity of L _ { X } = 1.7 \times 10 ^ { 35 } erg s ^ { -1 } ( for a distance of 6 kpc ) seems to require a huge kinetic energy of about 10 ^ { 50 } erg in the form of nonthermal particles to illuminate the cloud . The shock-acceleration at RX J1713.7 - 3946 can barely satisfy this energetic requirement , unless ( i ) the source is located much closer than the preferred distance of 6 kpc and/or ( ii ) the mechanical energy of the supernova explosion essentially exceeds 10 ^ { 51 } erg . Another possibility would be that an essential part of the lost energy due to the ionization and heating of gas , is somehow converted to plasma waves , which return this energy to nonthermal particles through their turbulent reacceleration on the plasma waves .