We discover a faint shell-type radio and X-ray source , G353.6-0.7 , associated with HESS J1731-347 . G353.6-0.7 is likely an old supernova remnant ( SNR ) , based on radio ( 0.8 GHz , 1.4 GHz and 5 GHz ) , infrared ( 8 \mu m from the GLIMPSE Legacy Project and 21 \mu m from the Midcourse Space Experiment ) , and X-ray ( 0.1 keV - 2.4 keV from the ROSAT survey and 5 - 20 keV from the INTEGRAL survey ) data . The SNR , centered at ( l , b ) = ( 353.55 , -0.65 ) with a radius of \sim 0.25 ^ { \circ } , closely matches the outline of the recently discovered extended TeV source HESS J1731-347 , which has no previously identified counterpart . A diffuse X-ray enhancement detected in the ROSAT all-sky survey is coincident with lower half shell of the SNR . Therefore the SNR is the best radio counterpart of both the HESS source and the diffuse X-ray enhancement . G353.6-0.7 has an age of \sim 27000 yrs . Altogether , the new discovery provides the best case that an old SNR emits TeV \gamma -rays . :