When metals are structured on nanometre length scales, their electrons are subject to confinement effects : the response of a confined electron gas is governed by Friedel oscillations(1) of the electron density and Rudermann-Kittel-Kasuya-Yosida oscillations(2) of the spin density, Spatial oscillations of electron density have been observed directly at surfaces (in the vicinity of defects and steps) by scanning tunnelling spectroscopy(3,4). But it has proved more difficult to probe such oscillations in bulk materials and over large distances(5). Here we report the detection of quantum oscillations in a three-dimensional electron gas confined to a half space by a surface, To facilitate this detection, we have inserted an atomically thin ferromagnetic cobalt film at a variable distance tau from the surface of a copper single crystal. The cobalt film induces(5) a total spin polarization P in the conduction electrons of the copper and, by virtue of the confining effects of the copper-vacuum interface, P varies as a function of tau. Our measurements of P reveal both quantum oscillations (the wavelengths of which are governed by the extremal diameters of the copper Fermi surface) and a decay with tau that are consistent with theoretical expectations(2). These observations show that a consequence of improving the quality of nanostructured materials is that long-range quantum interactions can emerge more effectively, so that even distant boundaries and defects can become pivotal in determining physical properties.