In-line holograms, or coherent shadow images, are formed in a scanning transmission electron microscopy (STEM) instrument when the electron probe of diameter 3 Å is focussed close to the specimen plane. If the beam axis is almost parallel to the flat face of a small crystal, bright spots and arcs appear in the shadow images as a result of the channelling of electrons along the surface layers of the crystal face. A bright, rather diffuse, axial spot is attributed to channelling directly along surface rows or planes of atoms. The localization of the channelling that gives the axial spot is demonstrated when a STEM image obtained by detecting the spot shows a single bright fringe, about 2 Å wide, at the crystal surface. Bright arcs, paralleling the curved shadow of the crystal edge, are seen to vary in intensity and sharpness with beam position. Evidence from the STEM images and the EELS spectra obtained from these bright arcs suggests that the arcs also arise from the channelling of electrons along the crystal surface.