We report on observations of the fading optical counterpart of the gamma-ray
burst GRB 970228, made with the Hubble Space Telescope STIS CCD approximately
six months after outburst and with the HST/NICMOS and Keck/NIRC approximately
one year after outburst. The unresolved counterpart is detected by STIS at
V=28.0 +/- 0.25, consistent with a continued power-law decline with exponent
-1.14 +/- 0.05. The counterpart is located within, but near the edge of, a
faint extended source with diameter ~0."8 and integrated magnitude V=25.8 +/-
0.25. A reanalysis of HST and NTT observations performed shortly after the
burst shows no evidence of proper motion of the point source or fading of the
extended emission. Only the extended source is visible in the NICMOS images
with a magnitude of H=23.3 +/- 0.1. The Keck observations find K = 22.8 +/-
0.3. Several distinct and independent means of deriving the foreground
extinction in the direction of GRB 970228 all agree with A_V = 0.75 +/- 0.2.
After adjusting for Galactic extinction, we find that the size of the observed
extended emission is consistent with that of galaxies of comparable magnitude
found in the Hubble Deep Field (HDF) and other deep HST images. Only 2% of the
sky is covered by galaxies of similar or greater surface brightness; therefore
the extended source is almost certainly the host galaxy. Additionally, we find
that the extinction-corrected V - H and V - K colors of the host are as blue as
any galaxy of comparable or brighter magnitude in the HDF. Taken in concert
with recent observations of GRB 970508, GRB 971214, and GRB 980703 our work
suggests that all four GRBs with spectroscopic identification or deep
multicolor broad-band imaging of the host lie in rapidly star-forming galaxies.Comment: 24 pages, Latex, 4 PostScript figures, to appear in the May 10 issue
of The Astrophysical Journal (Note: displayed abstract is abridged