We report on observations of the fading optical counterpart of the gamma-ra
y burst GRB 970228, made with the Hubble Space Telescope (HST) and the Keck
I telescope. The gamma-ray burst (GRB) was observed approximately 6 months
after outburst, on 1997 September 4, using the HST/STIS CCD, and approxima
tely 1 year after outburst, on 1998 February 24, using HST/NICMOS, and on 1
998 April 4 using the NIRC on Keck. The unresolved counterpart is detected
by STIS at V = 28.0 +/- 0.25, consistent with a continued power-law decline
with exponent -1.10 +/- 0.05. The counterpart is located within, but near
the edge of, a faint extended source with diameter similar to 0." 8 and int
egrated magnitude V = 25.8 +/- 0.25. A reanalysis of HST and New Technology
Telescope observations performed shortly after the burst shows no evidence
of proper motion of the point source or fading of the extended emission. A
lthough the optical transient is not detected in the NICMOS images (H great
er than or equal to 25.3), the extended source is visible and has a total m
agnitude H = 23.3 +/- 0.1. The Keck observations find K = 22.8 +/- 0.3. Com
parison with observations obtained shortly after outburst suggests that the
nebular luminosity has also been stable in the infrared. We find that seve
ral 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 adju
sting for this Galactic extinction, we find that the size of the observed e
xtended emission is consistent with that of galaxies of comparable magnitud
e found in the Hubble Deep Field (HDF) and other deep HST images. Only 2% o
f the sky is covered by galaxies of similar or greater surface brightness.
We therefore conclude that the extended source observed about GRB 970228 is
almost certainly its host galaxy. Additionally, we find that independent o
f assumed redshift, the host is significantly bluer than typical nearby blu
e dwarf irregulars. With the caveat that the presently available infrared o
bservations of the HDF are only fully complete to a limit about one-half ma
gnitude brighter than the host, we find that the extinction-corrected V-H a
nd V-K colors of the host are as blue as any galaxy of comparable or bright
er magnitude in the HDF. Taken in concert with recent observations of GRB 9
70508, GRB 971214, and GRB 980703 our work suggests that all four GRBs with
spectroscopic identification or deep multicolor broadband imaging of the h
ost lie in rapidly star-forming galaxies.