  This paper discusses the X-ray halo around the Swift gamma-ray burst GRB
050724 (z=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 200" 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 = 139 +/- 9 pc (from Earth) in a cloud/sheet of
thickness delta-D < 22 pc. The halo was observed only out to scattering angles
of 200", for which the scattering is dominated by the largest grains, with a
maximum size estimated to be a_max ~ 0.4-0.5 um. The scattering-to-extinction
ratio was estimated to be tau_scat/A_V > 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.
