  It is not clear whether gamma-ray bursts (GRBs) are unbiased tracers of
cosmic star formation at $z > 2$. Since dusty starburst galaxies are
significant contributors to the cosmic star formation at these redshifts, they
should form a major part of the GRB host population. However, recent studies at
$z \leq 2$ have shown that the majority of the star formation activity in GRB
hosts is not obscured by dust. Here, we investigate the galaxy-scale dust
obscuration in $z \sim 2-3.5$ GRB hosts pre-selected to have high-resolution,
high signal-to-noise afterglow spectra in the rest-frame ultraviolet (UV) and
thus relatively low line-of-sight dust obscuration. We present new deep VLA
observations of four GRB hosts, and compare the radio-based (upper limits on
the) "total" star formation rates (SFRs) to the "unobscured" SFRs derived from
fits to the optical-UV spectral energy distribution. The fraction of the total
SFR that is obscured by dust in these galaxies is found to be $<$ 90% in
general, and $\lesssim$ 50% for GRB 021004 in particular. These observations
suggest that $z \sim 2-3.5$ GRBs with UV-unobscured sightlines originate in
star-forming galaxies with low overall dust obscuration, unlike the dusty
starburst population.
