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Although water vapour is the main species observed in the coma of comet 67P/Churyumov–Gerasimenko and water is the major constituent of cometary nuclei, limited evidence for exposed water-ice regions on the surface of the nucleus has been found so far. The absence of large regions of exposed water ice seems a common finding on the surfaces of many of the comets observed so far. The nucleus of 67P/Churyumov–Gerasimenko appears to be fairly uniformly coated with dark, dehydrated, refractory and organic-rich material. Here we report the identification at infrared wavelengths of water ice on two debris falls in the Imhotep region of the nucleus. The ice has been exposed on the walls of elevated structures and at the base of the walls. A quantitative derivation of the abundance of ice in these regions indicates the presence of millimetre-sized pure water-ice grains, considerably larger than in all previous observations. Although micrometre-sized water-ice grains are the usual result of vapour recondensation in ice-free layers, the occurrence of millimetre-sized grains of pure ice as observed in the Imhotep debris falls is best explained by grain growth by vapour diffusion in ice-rich layers, or by sintering. As a consequence of these processes, the nucleus can develop an extended and complex coating in which the outer dehydrated crust is superimposed on layers enriched in water ice. The stratigraphy observed on 67P/Churyumov–Gerasimenko is therefore the result of evolutionary processes affecting the uppermost metres of the nucleus and does not necessarily require a global layering to have occurred at the time of the comet’s formation.