  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.
