We put stringent constraints for the first time on the dust properties in the circumburst medium of a gamma-ray burst (GRB) afterglow. This is based on the optical spectrum of GRB 020813 (z=1.255), obtained with Keck I LRIS 4.65 h after the burst. From the absorption lines in the spectrum, we derive very high column densities for six heavy elements with different refractory properties. The relative abundances resemble the dust depletion patterns in the Milky Way, from which we infer a visual extinction of A_V=0.4 and A_V>0.3 at 95% confidence level. However, the high columns of metals and dust contrast with an observed UV continuum spectrum that is remarkably close to a power law of the form F_nu propto nu^{-0.9}, with no sign of curvature, or a 2200 A extinction feature, suggesting low reddening. The Milky Way or Magellanic Cloud reddenings are possible only for very low visual extinctions (A_V<0.08 or A_V<0.2, respectively at 95% confidence), inconsistent with the A_V values inferred from the depletion analysis. If we assume a GRB intrinsic spectrum and an extinction law of the forms F_lambda^i = F_V (5500/lambda)^alpha and A_lambda= A_V (5500/lambda)^gamma, we obtain (for A_V=0.4) the constraints from continuum spectrum: gamma<0.85 and alpha<1.72.
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