This paper discusses the X-ray halo around the Swift -ray burst GRB 050724 (z 1⁄4 0:258), detected by the Swift X-Ray Telescope. The halo, which forms a ring around the fading X-ray source, expands to a radius of 20000 within 8 ks of the burst, exactly as expected for small-angle X-ray scattering by Galactic dust along the line of sight to a cosmologically distant GRB. The expansion curve and radial profile of the halo constrain the scattering dust to be concentrated at a distance of D 1⁄4 139 9 pc (from Earth) in a cloud/sheet of thickness D < 22 pc. The halo was observed only out to scattering angles of 20000, for which the scattering is dominated by the largest grains, with a maximum size estimated to be amax 0:4 0:5 m. The scattering-to-extinction ratio was estimated to be scat /AV k 0:022; this is a lower limit to the true value because contribution from smaller grains, which scatter to larger angles, was not directly observed. The line of sight to the GRB passes close to the Ophiuchus molecular cloud complex, which provides a plausible site for the scattering dust. Subject headingg s: dust, extinction — Galaxy: structure — gamma rays: bursts — X-rays: general Online material: color figures