  We imaged the field of GRB980329 in the optical and in the near-infrared
starting 20 hours after the event, at the ESO NTT, at the NOT, and at the
TIRGO. In the first night we detect an object of R = 23.6 +- 0.2 within the
BeppoSAX NFI error box at the same position as a transient VLA source proposed
as the radio afterglow of this GRB. The source faded by 1.6 +- 0.5 magnitudes
in 2.1 days, similarly to the decays of previous GRB optical afterglows. This
transient is likely the optical counterpart of GRB980329. In the near-infrared
we detect signal at 2-sigma significance, whose position is only marginally
consistent with that of the VLA source. The spectrum of the transient bears the
signatures of substantial absorption within the GRB host galaxy. The afterglow
energetics are interpreted as synchrotron radiation from an expanding blast
wave.
