Palladium oxide (PdO) is an excellent catalyst for the oxidation of CH4 and CO under oxygen-rich conditions. Unfortunately, however, many fundamental questions about the surface chemistry of PdO have remained unanswered since it has been challenging to prepare well-defined PdO surfaces for detailed experimental investigations. We investigated the adsorption of water on a PdO(101) thin film using temperature programmed desorption (TPD), isotope exchange measurements and density functional theory (DFT) calculations. TPD spectra obtained from high water coverages exhibit sharp peaks at 149 and 197 K that arise from water desorbing from a multilayer and a second layer, where the second layer appears to be stabilized by direct interactions with the PdO(101) surface. The TPD spectra also exhibit two peaks centered at 318 and 350 K that originate from different forms of chemisorbed water. Desorption orders determined from TPD spectra as well as H-D exchange experiments provide evidence that the peak at 350 K corresponds to dissociatively chemisorbed water, while the peak at 318 K arises from molecularly chemisorbed water. DFT calculations predict that dissociation is unfavorable for isolated H2O molecules, but is highly facile for water dimers and selectively produces HO-H2O dimers adsorbed along rows of coordinatively unsaturated (cus)-Pd atoms. Consistent with the TPD results, DFT also predicts that water begins to chemisorb only in molecular form when the total coverage exceeds 50% of the cus-Pd density. Finally, we find that uptake into the first-layer molecularly-chemisorbed state effectively ceases prior to saturation, and resumes only after the second-layer state nearly saturates. DFT suggests that strong orientation-dependent interactions between adsorbed species create unfavorable sites along the cus-Pd rows that hinder adsorption into the first layer when more than about 75% of the cus-Pd sites are occupied with adsorbed H2O and OH species. Overall, the results of this study may provide new insights for understanding how co-adsorbed water influences the activity of PdO surfaces in catalytic oxidation processes.