Hubble Space Telescope Imaging of the Optical Transient Associated with GRB970508

We report on Hubble Space Telescope (HST) observations of the optical transient (OT) discovered in the error box of the gamma-ray burst GRB970508. The object was imaged on 1997 June 2 with the Space Telescope Imaging Spectrograph (STIS) and Near-Infrared Camera and Multi-Object Spectrometer (NICMOS). The observations reveal a point-like source with R = 23.1 +- 0.2 and H = 20.6 +- 0.3, in agreement with the power-law temporal decay seen in ground-based monitoring. Unlike the case of GRB970228, no nebulosity is detected surrounding the OT of GRB970508. We set very conservative upper limits of R ~ 24.5 and H ~ 22.2 on the brightness of any underlying extended source. If this subtends a substantial fraction of an arcsecond, then the R band limit is ~25.5. In combination with Keck spectra that show Mg I absorption and [O II] emission at a redshift of z = 0.835, our observations suggest that the OT is located in a star-forming galaxy with total luminosity one order of magnitude lower than the knee of the galaxy luminosity function, L*. Such galaxies are now thought to harbor the majority of star formation at z ~ 1; therefore, these observations may provide support for a link between GRBs and star formation.