Understanding the correlation between structure and reactivity of oxide surfaces is vital for the rational design of catalytic materials. In this work, we demonstrate the exceptional degree of structure sensitivity of the water dissociation reaction for one of the most important materials in catalysis and electrocatalysis. We studied H2O on two atomically defined cobalt oxide surfaces, CoO(100) and Co3O4(111). Both surfaces are terminated by O2- and Co2+ in different coordination. By infrared reflection absorption spectroscopy and synchrotron radiation photoelectron spectroscopy we show that H2O adsorbs molecularly on CoO(100), while it dissociates and forms very strongly bound OH and partially dissociated (H2O) n(OH) m clusters on Co3O4(111). We rationalize this structure dependence by the coordination number of surface Co2+. Our results show that specific well-ordered cobalt oxide surfaces interact very strongly with H2O whereas others do not. We propose that this structure dependence plays a key role in catalysis with cobalt oxide nanomaterials.