Low signal to noise ratios and limited imaging depths restrict the ability of optical-imaging modalities to detect and accurately quantify molecular emissions from tissue. Here, by using a scanning external X-ray beam from a clinical linear accelerator to induce Cherenkov excitation of luminescence in tissue, we demonstrate in vivo mapping of the oxygenation of tumours at depths of several millimetres, with submillimetre resolution and nanomolar sensitivity. This was achieved by scanning thin sheets of the X-ray beam orthogonally to the emission-detection plane, and detecting the signal via a time-gated CCD camera synchronized to the radiation pulse. We also show with experiments using phantoms and with simulations that the performance of Cherenkov-excited luminescence scanned imaging (CELSI) is limited by beam size, scan geometry, probe concentration, radiation dose and tissue depth. CELSI might provide the highest sensitivity and resolution in the optical imaging of molecular tracers in vivo.