The interaction between aromatic rings and sulfur atoms in the side chains of amino acids is a factor in the formation and stabilization of alpha-helices in proteins. We studied the H2S-benzene dimer as the simplest possible prototype of sulfur-pi interactions. High-quality potential energy curves were obtained using coupled-cluster theory with single, double, and perturbative substitutions [CCSD(T)] and a large, augmented quadruple-zeta basis set (aug-cc-pVQZ). The equilibrium intermonomer distance for the hydrogens-down C2v configuration is 3.8 Angstrom with an interaction energy of -2.74 kcal/mol. Extrapolating the binding energy to the complete basis set limit gives -2.81 kcal/mol. This binding energy is comparable to that of H2O-benzene or of the benzene dimer, and the equilibrium distances is in close agreement with experiment. Other orientations of the dimer were also considered at less complete levels of theory. A considerable reduction in the binding for the sulfur-down configuration, together with an energy decomposition analysis, indicates that the attraction in H2S-benzene is best thought of as arising from a favorable electrostatic interaction between partially positive hydrogens in H2S with the negatively charged pi-cloud of the benzene.