THE presence of unseen haloes of ’dark matter’ has long been inferred from the high rotation speeds of gas and stars in the outer parts of spiral galaxies(1). The volume density of this dark matter decreases less quickly from the galactic centre than does that of the luminous mass (such as that in stars), meaning that the dark matter dominates the mass far from the centre(1,2). While searching for faint starlight away from the plane of the edge-on spiral galaxy NGC5907 (ref. 3), we have found that the galaxy is surrounded by a faint luminous halo. The intensity of light from this halo falls less steeply than any known luminous component of spiral galaxies, but is consistent with the distribution of dark mass inferred from the galaxy’s rotation curve.