The presence of substantial haloes of ’dark matter’ around galaxies has been inferred from their gravitational influence on the gas and stars in their disks’, but the nature of the dark matter remains very uncertain. The recent detection of faint optical emission from the halo around the edge-on galaxy NGC5907 (refs 2-5), distributed in a manner that follows the expected distribution of the gravitational mass, provided the first direct indication that faint stars might be the repository of some dark matter. But it was not clear how much of the mass was provided by these intrinsically faint stars. Here we report near-infrared observations of the halo emission from this galaxy. Taken together with the optical data, the results produce a very peculiar spectral energy distribution, which cannot be explained by any current models of stellar populations. The best approximation is a collection of stars with near-solar abundances of heavy elements, along with many low-mass stars. Such a population would be very unexpected for a galactic halo, where the stars should be old and have rather low fractions of heavy elements, but could account for much of the gravitational mass.