Within a cosmological hydrodynamical simulation, we form a disc galaxy with sub-components which can be assigned to a thin stellar disc, thick disc and a low-mass stellar halo via a chemical decomposition. The thin- and thick-disc populations so selected are distinct in their ages, kinematics and metallicities. Thin-disc stars are young (<6.6 Gyr), possess low velocity dispersion (σU, V, W = 41, 31, 25 km s−1), high [Fe/H] and low [O/Fe]. Conversely, the thick-disc stars are old (6.6 < age < 9.8 Gyr), lag the thin disc by ∼21 km s−1, possess higher velocity dispersion (σU, V, W = 49, 44, 35 km s−1) and have relatively low [Fe/H] and high [O/Fe]. The halo component comprises less than 4 per cent of stars in the ‘solar annulus’ of the simulation, has low metallicity, a velocity ellipsoid defined by σU, V, W = 62, 46, 45 km s−1 and is formed primarily in situ during an early merger epoch. Gas-rich mergers during this epoch play a major role in fuelling the formation of the old-disc stars (the thick disc). We demonstrate that this is consistent with studies which show that cold accretion is the main source of a disc galaxy's baryons. Our simulation initially forms a relatively short (scalelength ∼1.7 kpc at z = 1) and kinematically hot disc, primarily from gas accreted during the galaxy's merger epoch. Far from being a competing formation scenario, we show that migration is crucial for reconciling the short, hot, discs which form at high redshift in Λ cold dark matter, with the properties of the thick disc at z = 0. The thick disc, as defined by its abundances, maintains its relatively short scalelength at z = 0 (2.31 kpc) compared with the total disc scalelength of 2.73 kpc. The inside-out nature of disc growth is imprinted in the evolution of abundances such that the metal-poor α-young population has a larger scalelength (4.07 kpc) than the more chemically evolved metal-rich α-young population (2.74 kpc).