The mineral greigite, Fe3S4, shows promising electro-reduction activity, especially towards carbon dioxide conversion to small organic molecules. We have employed density functional theory calculations with correction for the long-range dispersion forces to investigate the behavior of hydrogen on the greigite{111} surface. We have studied the adsorption, diffusion, surface reduction and associative (i.e. Volmer-Tafel mechanism) and molecular desorption of hydrogen as a function of its coverage. We found that (i) the H ad-atoms adsorb on S sites far from metallic centres in the topmost surface layer; (ii) the reduction of greigite by hydrogen is energetically unfavorable at any surface coverage; and (iii) molecular hydrogen evolution has a transition state at ∼0.5 eV above the energy of the reactants on Fe3S4{111}, which is very similar to the barrier found experimentally on Pt{111}. We have also determined the electrode potential under room conditions at which the H2 evolution reaction becomes energetically barrierless.