We analyse the structure and chemical enrichment of a Milky Way-like galaxy with a stellar mass of 2 10^{10} M_sun, formed in a cosmological hydrodynamical simulation. It is disk-dominated with a flat rotation curve, and has a disk scale length similar to the Milky Ways, but a velocity dispersion that is ~50% higher. Examining stars in narrow [Fe/H] and [alpha/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 scale length, while the young stars form a thinner disk, with scale lengths decreasing, as [Fe/H] increases. b) Consequently, there is a distinct outward metallicity gradient. c) Mono-abundance populations exist with a continuous distribution of scale heights (from thin to thick). However, the simulated galaxy has a distinct and substantive very thick disk (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.