Chitosan, an environmentally friendly and highly bio-producible material, is a potential proton-conducting electrolyte for use in fuel cells. Thus, to microscopically elucidate proton transport in hydrated chitosan, we employed the quasi-elastic neutron scattering (QENS) technique. QENS analysis showed that the hydration water, which was mobile even at 238 K, moved significantly more slowly than the bulk water, in addition to exhibiting jump diffusion. Furthermore, upon increasing the temperature from 238 to 283 K, the diffusion constant of water increased from 1.33 × 10−6 to 1.34 × 10−5 cm2/s. It was also found that a portion of the hydrogen atoms in chitosan undergo a jump-diffusion motion similar to that of the hydrogen present in water. Moreover, QENS analysis revealed that the activation energy for the jump-diffusion of hydrogen in chitosan and in the hydration water was 0.30 eV, which is close to the value of 0.38 eV obtained from the temperature-dependent proton conductivity results. Overall, it was deduced that a portion of the hydrogen atoms in chitosan dissociate and protonate the interacting hydration water, resulting in the chitosan exhibiting proton conductivity.