The redshift of GRB 970508

GRB 970508 is the second gamma-ray burst (GRB) for which an optical afterglow has been detected. It is the first GRB for which a distance scale has been determined: absorption and emission features in spectra of the optical afterglow place GRB 970508 at a redshift of z greater than or equal to 0.835. The lack of a Ly alpha forest in these spectra further constrains this redshift to be less than z similar to 2.3. I show that the spectrum of the optical afterglow of GRB 970508, once corrected for Galactic absorption, is inconsistent with the relativistic blast-wave model unless a second, redshifted source of extinction is introduced. This second source of extinction may be the yet unobserved host galaxy. I determine its redshift to be z = 1.09(-0.41)(+0.14), which is consistent with the observed redshift of z = 0.835. Redshifts greater than z = 1.40 are ruled out at the 3 sigma confidence level.