We report the discovery of the optical and radio afterglow of GRB 010921, the first gamma-ray burst afterglow to be found from a localization by the High Energy Transient Explorer satellite. We present optical spectroscopy of the host galaxy, which we find to be a dusty and apparently normal star-forming galaxy at z=0.451. The unusually steep optical spectral slope of the afterglow can be explained by heavy extinction, A$_V$>0.5 mag, along the line of sight to the GRB. Dust with similar A$_V$ for the host galaxy as a whole appears to be required by the measurement of a Balmer decrement in the spectrum of the host galaxy.