Adsorption on various adsorbents of hydrogen and helium at temperatures close to their boiling points shows, in some cases, unusually high monolayer capacities. The microscopic nature of these adsorbate phases at low temperatures has, however, remained challenging to characterize. Here, using high-resolution cryo-adsorption studies together with characterization by inelastic neutron scattering vibration spectroscopy, we show that, near its boiling point (~20 K), H₂ adsorbed on a well-ordered mesoporous silica forms a two-dimensional monolayer with a density more than twice that of bulk-solid H₂, rather than a bilayer. Theoretical studies, based on thorough first-principles calculations, rationalize the formation of such a super-dense phase. The strong compression of the hydrogen surface layer is due to the excess of surface–hydrogen attraction over intermolecular hydrogen repulsion. Use of this super-dense hydrogen monolayer on an adsorbent might be a feasible option for the storage of hydrogen near its boiling point, compared with adsorption at 77 K.