High-resolution transmission electron microscopy images of room-temperature fluid xenon in small faceted cavities in aluminum reveal the presence of three well-defined layers within the fluid at each facet. Such interfacial layering of simple liquids has been theoretically predicted, but observational evidence has been ambiguous. Molecular dynamics simulations indicate that the density variation induced by the layering will cause xenon, confined to an approximately cubic cavity of volume approximately 8 cubic nanometers, to condense into the body-centered cubic phase, differing from the face-centered cubic phase of both bulk solid xenon and solid xenon confined in somewhat larger (>/=20 cubic nanometer) tetradecahedral cavities in face-centered cubic metals. Layering at the liquid-solid interface plays an important role in determining physical properties as diverse as the rheological behavior of two-dimensionally confined liquids and the dynamics of crystal growth.