The host galaxy of GRB 970508

We present late-time imaging and spectroscopic observations of the optical transient (OT) and host galaxy of 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 that we identify with [O II] lambda 3727 and [Ne III] lambda 3869 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 mas or a projected radial separation of less than 2.7 kpc. The luminosity of the [O Ir] line implies a minimum star formation rate of 1 M-. yr(-1). In our assumed cosmology, the implied rest-frame 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 OT requires that at least some fraction of gamma-ray burst progenitors are not ejected in even the weakest galactic potentials.