The shell-type supernova remnant HESS J1731 - 347 emits TeV gamma-rays , and is a key object for the study of the cosmic ray acceleration potential of supernova remnants . We use 0.5-1 arcminute Mopra CO/CS ( 1-0 ) data in conjunction with HI data to calculate column densities towards the HESS J1731 - 347 region . We trace gas within at least four Galactic arms , typically tracing total ( atomic+molecular ) line-of-sight H column densities of 2-3 \times 10 ^ { 22 } cm ^ { -2 } . Assuming standard X-factor values and that most of the HI/CO emission seen towards HESS J1731 - 347 is on the near-side of the Galaxy , X-ray absorption column densities are consistent with HI+CO-derived column densities foreground to , but not beyond , the Scutum-Crux Galactic arm , suggesting a kinematic distance of \sim 3.2 kpc for HESS J1731 - 347 . At this kinematic distance , we also find dense , infrared-dark gas traced by CS ( 1-0 ) emission coincident with the north of HESS J1731 - 347 , the nearby HII region G353.43 - 0.37 and the nearby unidentified gamma-ray source HESS J1729 - 345 . This dense gas lends weight to the idea that HESS J1729 - 345 and HESS J1731 - 347 are connected , perhaps via escaping cosmic-rays .