We report on observations of the fading optical counterpart of the gamma-ray burst GRB 970228 , made with the Hubble Space Telescope and the Keck I telescope .
The GRB was observed approximately six months after outburst , on 4 September 1997 , using the HST/STIS CCD , and approximately one year after outburst , on 24 February 1998 , using HST/NICMOS , and on 4 April 1998 using the NIRC on Keck .
The unresolved counterpart is detected by STIS at V = 28.0 \pm 0.25 , consistent with a continued power-law decline with exponent -1.10 \pm 0.10 .
The counterpart is located within , but near the edge of , a faint extended source with diameter \sim 0 \farcs 8 and integrated magnitude V = 25.8 \pm 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 .
Although the optical transient ( OT ) is not detected in the NICMOS images ( \hbox { $ H$ } \geq 25.3 ) , the extended source is visible and has a total magnitude \hbox { $ H$ } = 23.3 \pm 0.1 .
The Keck observations find \hbox { $ K$ } = 22.8 \pm 0.3 .
Comparison with observations obtained shortly after outburst suggests that the nebular luminosity has also been stable in the infrared .

We find that several distinct and independent means of deriving the foreground extinction in the direction of GRB 970228 all agree with A _ { V } = 0.75 \pm 0.2 .
After adjusting for this 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 .
We therefore conclude that the extended source observed about GRB 970228 is almost certainly its host galaxy .
Additionally , we find that independent of assumed redshift , the host is significantly bluer than typical nearby blue dwarf irregulars .
With the caveat that the presently available infrared observations of the HDF are only fully complete to a limit about one-half magnitude brighter than the host , we find that the extinction-corrected \hbox { $ V$ } - \hbox { $ H$ } and \hbox { $ V$ } - \hbox { $ 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 .