Although perovskite oxides hold promise in applications ranging from solid oxide fuel cells to catalysts, their surface chemistry is poorly understood at the molecular level. Here we follow the formation of the first monolayer of water at the ( 001) surfaces of Srn+1RunO3n+1 (n = 1, 2) using low-temperature scanning tunnelling microscopy, X-ray photoelectron spectroscopy, and density functional theory. These layered perovskites cleave between neighbouring SrO planes, yielding almost ideal, rocksalt-like surfaces. An adsorbed monomer dissociates and forms a pair of hydroxide ions. The OH stemming from the original molecule stays trapped at Sr-Sr bridge positions, circling the surface OH with a measured activation energy of 187 +/- 10meV. At higher coverage, dimers of dissociated water assemble into one-dimensional chains and form a percolating network where water adsorbs molecularly in the gaps. Our work shows the limitations of applying surface chemistry concepts derived for binary rocksalt oxides to perovskites.