  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 >= 0.835 [1,2]. The lack of a
Lyman-alpha forest in these spectra further constrains this redshift to be less
than approximately 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^{+0.14}_{-0.41}, 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.
