We present late-time imaging and spectroscopic observations of the optical transient ( OT ) of gamma-ray burst ( GRB ) 970508 .
Imaging observations roughly 200 and 300 days after the burst provide unambiguous evidence for the flattening of the light-curve .
The spectroscopic observations reveal two persistent features which we identify with [ O II ] 3727 Å and [ Ne III ] 3869 Å at a redshift of z = 0.835 -- - the same redshift as the absorption system seen when the transient was bright .
The OT was coincident with the underlying galaxy to better than 370 milliarcsec or a projected radial separation of less than 2.7 kpc .
The luminosity of the [ O II ] line implies a minimum star-formation rate of \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ > $ } } } 1 ~ { % } M _ { \odot } ~ { } { yr } ^ { -1 } .
In our assumed cosmology , the implied restframe absolute magnitude is M _ { B } = -18.55 , or L _ { B } = 0.12 L _ { * } .
This object , the likely host of GRB 970508 , can thus be characterized as an actively star-forming dwarf galaxy .
The close spatial connection between this dwarf galaxy and the GRB requires that at least some fraction of progenitors be not ejected in even the weakest galactic potentials .