We report on Hubble Space Telescope/ACS photometry of the rich intermediate-age star cluster NGC 1846 in the Large Magellanic Cloud, which clearly reveals the presence of a double main-sequence turn-off in this object. Despite this, the main-sequence, subgiant branch and red giant branch are all narrow and well defined, and the red clump is compact. We examine the spatial distribution of turn-off stars and demonstrate that all belong to NGC 1846 rather than to any field star population. In addition, the spatial distributions of the two sets of turn-off stars may exhibit different central concentrations and some asymmetries. By fitting isochrones, we show that the properties of the colour-magnitude diagram can be explained if there are two stellar populations of equivalent metal abundance in NGC 1846, differing in age by ~300 Myr. The absolute ages of the two populations are ∼1.9 and ∼2.2 Gyr, although there may be a systematic error of up to ±0.4 Gyr in these values. The metal abundance inferred from isochrone fitting is [M/H] ~ -0.40, consistent with spectroscopic measurements of [Fe/H]. We propose that the observed properties of NGC 1846 can be explained if this object originated via the tidal capture of two star clusters formed separately in a star cluster group in a single giant molecular cloud. This scenario accounts naturally for the age difference and uniform metallicity of the two member populations, as well as the differences in their spatial distributions.