  Supernova remnants act as particle accelerators, providing the cosmic-ray
protons that permeate the interstellar medium and initiate the ion-molecule
reactions that drive interstellar chemistry. Enhanced fluxes of cosmic-ray
protons in close proximity to supernova remnants have been inferred from
observations tracing particle interactions with nearby molecular gas. Here I
present observations of H$_3^+$ and CO absorption, molecules that serve as
tracers of the cosmic-ray ionization rate and gas density, respectively, in
sight lines toward the W28 and Vela supernova remnants. Cosmic-ray ionization
rates inferred from these observations range from about 2--10 times the average
value in Galactic diffuse clouds ($\sim 3\times10^{-16}$ s$^{-1}$), suggesting
that the gas being probed is experiencing an elevated particle flux. While it
is difficult to constrain the line-of-sight location of the absorbing gas with
respect to the supernova remnants, these results are consistent with a scenario
where cosmic rays are diffusing away from the acceleration site and producing
enhanced ionization rates in the surrounding medium.
