We investigated the effects of gaseous hydrogen exposure on the bare MoS2 and Pd-deposited MoS2 basal surfaces using ambient-pressure X-ray photoelectron spectroscopy. In the Mo 3d core-level, S 2p core-level, and valence-band photoelectron spectra of a bare MoS2 surface, little change was observed in the energy shift before and after exposure to hydrogen gas. Upon hydrogen gas exposure on the Pd-deposited MoS2 surface, each peak in the photoelectron spectra (Mo 3d, S 2p, and valence-band) shifted to a lower binding energy with 0.1 eV. When hydrogen gas was evacuated, the peak energy remained lower compared with that before hydrogen gas exposure. The Pd 3d XPS spectra changed upon hydrogen gas exposure, which can be interpreted as the adsorption of dissociated hydrogen atoms on the Pd sites. These results indicate that the dissociation of molecular hydrogen and the adsorption of atomic hydrogen occur on the Pd-deposited sites on MoS2, and thereafter hydrogen atoms spillover onto the MoS2 surface. This study shows that the activation site for the dissociation of molecular hydrogen is created on an inert MoS2 basal surface by Pd deposition. In addition, the electronic states of the MoS2 substrate have been modulated by hydrogen atoms spilled over onto the MoS2 surface.