  We report on observations of the fading optical counterpart of the gamma-ray
burst GRB 970228, made on 4~September~1997 using the STIS CCD on the Hubble
Space Telescope. The unresolved counterpart is detected at V=28 +/- 0.25,
consistent with a continued power-law decline with exponent -1.14 +/- 0.05. No
proper motion is detected, in contradiction of an earlier claim. The
counterpart is located within, but near the edge of, a faint extended source
with diameter ~0."8 and integrated magnitude 25.7 +/- 0.25. Comparison with
WFPC2 data taken one month after the initial burst and NTT data taken on March
13 shows no evidence for fading of the extended emission.
  After adjusting for the probable Galactic extinction in the direction of GRB
970228 of A_v=0.7, we find that the observed nebula is consistent with the
sizes of galaxies of comparable magnitude found in the Hubble Deep Field and
other deep HST images, and that only 2% of the sky is covered by galaxies of
similar or greater surface brightness. We therefore conclude that the extended
source observed about GRB 970228 is most likely a galaxy at moderate redshift,
and is almost certainly the host of the gamma-ray burst.
