H2S adsorption and dissociation on the gallium-rich GaAs( 001)- 4 x 2 surface is investigated using hybrid density functional theory. Starting from chemisorbed H2S on the GaAs( 001)- 4 x 2 surface, two possible reaction routes have been proposed. We find that H2S adsorbs molecularly onto GaAs( 001)- 4 x 2 via the formation of a dative bond, and this process is exothermic with adsorption energy of 6.6 kcal/mol. For the first reaction route, one of the H atoms from the chemisorbed H2S is transferred to a second-layer As atom and the dissociated SH is inserted into the Ga-As bond with an activation barrier of 8.2 kcal/mol, which is found to be 29.3 kcal/mol more stable than the reactants. For the second case, the dissociated species may insert themselves into the Ga-Ga dimer resulting in the Ga-H-Ga and Ga-HS-Ga bridge-bonded states, which are found to be 29.8 and 22.2 kcal/mol more stable than the reactants, respectively. However, the calculations also show that the activation barrier (16.1 kcal/mol) for chemisorbed H2S dissociation through the second route is higher than the transfer of one H atom into a second-layer As atom. As a result, we conclude that sulfur insertion into the Ga-As bond is more kinetically favorable.