Cosmic rays pervade the Galaxy and are thought to be accelerated in supernova shocks. The interaction of cosmic rays with dense interstellar matter has two important effects: 1) high energy (>1 GeV) protons produce {\gamma}-rays by {\pi}0-meson decay; 2) low energy (< 1 GeV) cosmic rays (protons and electrons) ionize the gas. We present here new observations towards a molecular cloud close to the W51C supernova remnant and associated with a recently discovered TeV {\gamma}-ray source. Our observations show that the cloud ionization degree is highly enhanced, implying a cosmic ray ionization rate ~ 10-15 s-1, i.e. 100 times larger than the standard value in molecular clouds. This is consistent with the idea that the cloud is irradiated by an...