We imaged the X-ray error box of GRB 980703, beginning 22.5 hr after the ga
mma-ray event, in both the optical R and near-infrared H bands. A fading op
tical/IR object was detected within the X-ray error box, coincident with th
e variable radio source reported by Frail et al. in 1998, who also detected
the optical transient independently of us. Further imagery revealed the ga
mma-ray burst (GRB) host galaxy, with R = 22.49 +/- 0.04 and H = 20.5 +/- 0
.25, the brightest so far detected. When excluding its contribution to the
total flux, both the R- and H-band light curves are well fit by a power-law
decay with index alpha similar or equal to 1.4. Our data suggest an intrin
sic column density in the host galaxy of similar to 3.5 x 10(21) cm(-2), wh
ich indicates the existence of a dense and gas-rich medium in which the GRB
occurred, thus supporting the hypernova model scenarios.