We report on HST/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, sub-giant 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 approximately 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.