Water dissociation on copper is one of the rate-limiting steps in the water-gas-shift (WGS) reaction. Copper atoms dispersed evenly from freshly made catalyst segregate to form clusters under the WGS operating conditions. Using density functional theory, we have examined water adsorption and dissociation on the smallest stable 3-dimensional copper cluster, Cu(7). Water molecules are adsorbed on the cluster sequentially until full saturation at which no direct water-copper contact is sterically possible. The adsorption is driven mainly by the overlap between the p-orbital of O atom occupied by the lone pair and the 3d-orbitals of copper, from which a fractional charge is promoted to the 4s-orbital to accommodate the charge transfer from water. Water dissociation on the Cu(7) cluster was investigated at both low and high water coverage. It was found that water dissociation into OH and H is exothermic but is inherently a high temperature process at low coverage. At high coverage, the reaction becomes more exothermic with fast kinetics. In both cases, water can catalyze the reaction. It was found that direct dissociation of the OH species is endothermic with a significantly higher barrier at both low and high coverage. However, the OH species can readily react with another adjacent hydroxyl group to form an O adatom and water molecule. Our studies indicate that the basic chemical properties of water dissociative chemisorption may not change significantly with the size of small copper clusters. Similarities between water dissociation on copper clusters and on copper crystalline surfaces are discussed.