We used Hubble Space Telescope observations to study the young cluster NGC 1844 in the Large Magellanic Cloud (LMC). We estimated the fraction and the mass-ratio distribution of photometric binaries and report that the main sequence presents an intrinsic breadth which cannot be explained only in terms of photometric errors, and is unlikely because of differential reddening. We attempted different interpretations of this feature, including stellar rotation, binary stars, and the presence of multiple stellar populations of different ages, metallicity, helium, or C+N+O abundance. Although we have excluded age, helium, and C+N+O variations of being responsible for the main-sequence spread, none of the other interpretations is conclusive. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555, under GO-12219.Figures 1-3, 9, and 10 are available in electronic form at http://www.aanda.orgPhotometric data is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/555/A143