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We report on observations of the fading optical counterpart of the gamma-rayburst GRB 970228, made with the Hubble Space Telescope STIS CCD approximatelysix months after outburst and with the HST/NICMOS and Keck/NIRC approximatelyone year after outburst. The unresolved counterpart is detected by STIS atV=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, afaint extended source with diameter ~0."8 and integrated magnitude V=25.8 +/-0.25. A reanalysis of HST and NTT observations performed shortly after theburst shows no evidence of proper motion of the point source or fading of theextended emission. Only the extended source is visible in the NICMOS imageswith 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 foregroundextinction 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 observedextended emission is consistent with that of galaxies of comparable magnitudefound in the Hubble Deep Field (HDF) and other deep HST images. Only 2% of thesky is covered by galaxies of similar or greater surface brightness; thereforethe extended source is almost certainly the host galaxy. Additionally, we findthat the extinction-corrected V - H and V - K colors of the host are as blue asany galaxy of comparable or brighter magnitude in the HDF. Taken in concertwith recent observations of GRB 970508, GRB 971214, and GRB 980703 our worksuggests that all four GRBs with spectroscopic identification or deepmulticolor 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

The Fading Optical Counterpart of GRB 970228, 6 Months and 1 Year Later