  We report on the discovery of a variable radio source, VLA J070238.0+385044,
associated with the proposed x-ray counterpart, 1SAX J0702.6+3850 of GRB
980329. The source was monitored from one day after the burst to one month
later at centimeter wavelengths (1.4, 4.9, 8.3 and 15 GHz; Very Large Array --
VLA), and in the 3-mm band (90 GHz; Owen Valley Radio Observatory -- OVRO).
Based on its variability, compactness and spectrum, we identify VLA
J070238.0+385044 as the afterglow from GRB 980329. We interpret the rapid flux
density variations as interstellar scintillation and the sharp turnover in the
radio spectrum below 13 GHz as arising from synchrotron self-absorption. This
suggests that the angular diameter of the fireball from GRB 980329 was of order
a few microarcseconds in the first two weeks. The absence of a readily
detectable afterglow in the optical, but clear detections in both the radio and
infrared, can be understood as the result of extinction by dust. In this
context it is interesting to note that half of all well-localized gamma-ray
bursts have no optical counterpart. Based on our study of GRB 980329 we suggest
that the progenitors of a sizable fraction of gamma-ray bursts are associated
with regions of moderate to high gas density.
