The hydrogen abstraction reaction H2S + OH -> H2O + SH has been studied using the "gold standard" CCSD(T) method along with the Dunning's aug-cc-pVXZ (up to 5Z) basis sets. For the reactant (entrance) complex, the CCSD(T) method predicts a HSH center dot center dot center dot OH hydrogen-bonded structure to be lowest-lying, and the other lower-lying isomers, including the two-center three-electron hemibonded structure H2S center dot center dot center dot OH, have energies within 2 kcal/mol. The similar situation is for the product (exit) complex. With the aug-cc-pV5Z single point energies at the aug-cc-pVQZ geometry, the dissociation energy for the reactant complex to the reactants (H2S + OH) is predicted to be 3.37 kcal/mol, and that for the product complex to the products (H2O + SH) is 2.92 kcal/mol. At the same level of theory, the classical barrier height is predicted to be only 0.11 kcal/mol. Thus, the OH radical will react promptly with H2S in the atmosphere. We have also tested the performance of 29 density functional theory (DFT) methods for this reaction. Most of them can reasonably predict the reaction energy, but the different functional give quite different energy barriers, ranged from -10.3 to +2.8 kcal/mol, suggesting some caution in choosing density functionals to explore the PES of chemical reactions.