The Orion Bar is the archetypal edge-on molecular cloud surface illuminated by strong ultraviolet radiation from nearby massive stars. Owing to the close distance to Orion (about 1,350 light-year), the effects of stellar feedback on the parental cloud can be studied in detail. Visible-light observations of the Bar1 show that the transition between the hot ionised gas and the warm neutral atomic gas (the ionisation front) is spatially well separated from the transition from atomic to molecular gas (the dissociation front): about 15 arcseconds or 6,200 astronomical units. (One astronomical unit is the Earth-Sun distance.) Static equilibrium models2,3 used to interpret previous far-infrared and radio observations of the neutral gas in the Bar4,5,6 (typically at 10-20 arcsecond resolution) predict an inhomogeneous cloud structure consisting of dense clumps embedded in a lower density extended gas component. Here we report 1 arcsecond resolution millimetre-wave images that allow us to resolve the molecular cloud surface and constrain the gas density and temperature structures at small spatial scales. In contrast to stationary model predictions7,8,9, there is no appreciable offset between the peak of the H2 vibrational emission (delineating the H/H2 transition) and the edge of the observed CO and HCO+ emission. This implies that the H/H2 and C+/C/CO transition zones are very close. These observations reveal a fragmented ridge of high-density substructures, photo-ablative gas flows and instabilities at the molecular cloud surface. They suggest that the cloud edge has been compressed by a high-pressure wave that currently moves into the molecular cloud. The images demonstrate that dynamical and nonequilibrium effects are important. Thus, they should be included in any realistic description of irradiated interstellar matter.