It is widely believed that small gold clusters supported on an oxide surface and adsorbed at the site of an oxygen vacancy are negatively charged. It has been suggested that this negative charge helps a gold cluster adsorb oxygen and weakens the O-O bond to make oxidation reactions more efficient. Given the fact that an oxygen vacancy is electron rich and that Au is a very electronegative element, the assumption that the Au cluster will take electron density from the vacancy is plausible. However, the density functional calculations presented here show that the situation is more complicated. The authors have used the Bader method to examine the charge redistribution when a Aun cluster (n=1-7) binds next to or at an oxygen vacancy on rutile TiO2(110). For the lowest energy isomers they find that Au1 and Au3 are negatively charged, Au5 and Au7 are positively charged, and Au2, Au4, and Au6 exchange practically no charge. The behavior of the Aun isomers having the second-lowest energy is also unexpected. Au2, Au3, Au5, and Au7 are negatively charged upon adsorption and very little charge is transferred when Au4 and Au6 are adsorbed. These observations can be explained in terms of the overlap between the frontier molecular orbitals of the gold cluster and the eigenstates of the support. Aun with even n becomes negatively charged when the lowest unoccupied molecular orbital has a lobe pointing in the direction of the oxygen vacancy or towards a fivefold coordinated Ti (5c-Ti) located in the surface layer; otherwise it stays neutral. Aun with odd n becomes negatively charged when the singly occupied molecular orbital has a lobe pointing in the direction of a 5c-Ti located at the vacancy site or in the surface layer, otherwise it donates electron density into the conduction band of rutile TiO2(110) becoming positively charged.