We analyse the structure and chemical enrichment of a Milky Way-like galaxy with a stellar mass of 2 × 1010 M, formed in a cosmological hydrodynamical simulation. It is disc dominated with a flat rotation curve, and has a disc scalelength similar to the Milky Way's, but a velocity dispersion that is ∼50 per cent higher. Examining stars in narrow Fe/H and α/Fe abundance ranges, we find remarkable qualitative agreement between this simulation and observations. (a) The old stars lie in a thickened distribution with a short scalelength, while the young stars form a thinner disc, with scalelengths decreasing, as Fe/H increases. (b) Consequently, there is a distinct outward metallicity gradient. (c) Mono-abundance populations exist with a continuous distribution of scaleheights (from thin to thick). However, the simulated galaxy has a distinct and substantive very thick disc (h z ∼ 1.5 kpc), not seen in the Milky Way. The broad agreement between simulations and observations allows us to test the validity of observational proxies used in the literature: we find in the simulation that mono-abundance populations are good proxies for single age populations (<1 Gyr) for most abundances.