The analysis(1) of gravitational microlensing events of stars(2,3) in the Large Magellanic Cloud places the masses of the lensing objects in the range 0.3-0.8 solar masses, suggesting that they might be old white-dwarf stars, Such objects represent the last stage of stellar evolution : they are the cooling cores of stars that have Lost their atmospheres after nuclear fusion has ceased in their centres. If white dwarfs exist in abundance in the halo of our Galaxy, this would have profound implications for our understanding of the early generations of stars in the Universe(4-6). Previous attempts to constrain theoretically(6-8) the contribution of white dwarfs to microlensing indicate that they can account for only a small fraction of the events. But these estimates relied on models of white-dwarf cooling that are inadequate for describing the properties of the oldest such objects. Here I present cooling models appropriate for very old white I dwarfs. I find, using these models, that the widely held notion that old white dwarfs are red applies only to those with a helium atmosphere; old white dwarfs with hydrogen atmospheres, which could be a considerable fraction of the total population, will appear rather blue, with colours similar to those of the faint blue sources in the Hubble Deep Field. Observational searches for the population of microlensing objects should therefore look for faint blue objects, rather than faint red ones.