White dwarfs are the remnant cores of stars that initially had masses of less than 8 solar masses. They cool gradually over billions of years, and have been suggested to make up much of the 'dark matter' in the halo of the Milky Way. But extremely cool white dwarfs have proved difficult to detect, owing to both their faintness and their anticipated similarity in colour to other classes of dwarf stars. Recent improved models indicate that white dwarfs are much more blue than previously supposed, suggesting that the earlier searches may have been looking for the wrong kinds of objects. Here we report an infrared spectrum of an extremely cool white dwarf that is consistent with the new models. We determine the star's temperature to be 3,500 +/- 200 K, making it the coolest known white dwarf. The kinematics of this star indicate that it is in the halo of the Milky Way, and the density of such objects implied by the serendipitous discovery of this star is consistent with white dwarfs dominating the dark matter in the halo.