Using density functional theory with and without Hubbard-U correction we have calculated the geometric structure and the binding energy of H₂S molecules adsorbed on the main cleavage plane of ZnO. We find that H₂S molecules preferentially dissociate upon adsorption, with a negligible barrier for the first and an activation energy of about 0.5 eV for the second SH bond dissociation. In the low coverage limit of individual molecules single and double dissociation are energetically almost degenerate. At higher coverage double dissociation is favored because of attractive adsorbate–adsorbate interactions. Thermodynamic analysis shows that the double-dissociated state at full saturation with a coverage of 1/2 monolayer is the most stable adsorbate structure for a wide range of temperatures and partial pressures. However, at high H₂S chemical potential a full monolayer of single-dissociated H₂S becomes thermodynamically more favorable. In addition, at low temperature this structure may exist as a metastable configuration due to the activation barrier for the second SH bond cleavage. Finally we show that it is thermodynamically favorable for adsorbed H₂S to react with the first ZnO surface layer to form ZnS and water.