We report on observations of the field of GRB 970508 made in early August 1998 , 454 days after outburst , with the STIS CCD camera onboard the Hubble Space Telescope . The images , taken in open filter ( 50CCD ) mode , clearly reveal the presence of a galaxy which was obscured in earlier ( June 1997 ) HST images by emission from the optical transient ( OT ) . The galaxy is regular in shape : after correcting for the HST/STIS PSF , it is well-fitted by an exponential disk with a scale length of 0 \farcs 046 \pm 0 \farcs 006 and an ellipticity of 0.70 \pm 0.07 . All observations are marginally consistent with a continuous decline in OT emission as t ^ { -1.3 } beginning two days after outburst ; however , we find no direct evidence in the HST image for emission from the OT , and the surface brightness profile of the galaxy is most regular if we assume that the OT emission is negligible , suggesting that the OT may have faded more rapidly at late times than is predicted by the power-law decay . Due to the wide bandwidth of the STIS clear mode , the estimated magnitude of the galaxy is dependent on the galaxy spectrum that is assumed . Using colors obtained from late-time ground-based observations to constrain the spectrum , we find V = 25.4 \pm 0.15 , a few tenths of a magnitude brighter than earlier ground-based estimates that were obtained by observing the total light of the galaxy and the OT and then subtracting the estimated OT brightness assuming it fades as a single power-law . This again suggests that the OT may have faded faster at late time than the power-law predicts . The position of the OT agrees with that of the isophotal center of the galaxy to 0 \farcs 01 which , at the galaxy redshift z = 0.83 , corresponds to an offset from the center of the host of \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 70 pc . This remarkable agreement raises the possibility that the GRB may have been associated with either an active galactic nucleus or a nuclear starburst .