We have studied the structure of mononuclear gold supported on acidic form of faujasite zeolite in two oxidation states, namely, 0 and +1, using density functional theory. The binding of the gold monomer to the zeolite support is stronger in the oxidation state +1 than in the oxidation state 0. For the oxidation state 0, the hydrogenated clusters AuH/(2H)-FAU, AuH2/H-FAU generated by stepwise reverse hydrogen spillover from bridging OH groups of zeolite are energetically preferred over the Au/(3H)-FAU structure. Reverse hydrogen spillover of all the three acidic protons from the zeolite to the Au monomer did not lead to a stable structure. The calculated reverse hydrogen spillover energy per hydrogen atom for zeolite supported AuH and AuH2 clusters are −10.2 and −5.1 kJ/mol, respectively, in the oxidation state 0, while in the oxidation state +1 it is 20.9 kJ/mol for zeolite supported Au+H cluster.