  We discuss the first results of our ongoing program of Target of Opportunity
observations of gamma-ray bursts (GRBs) using the SCUBA instrument on the James
Clerk Maxwell Telescope. We present the results for GRB 970508, 971214, 980326,
980329, 980519, and 980703.
  Our most important result to date is the detection of a fading counterpart to
GRB 980329 at 850 microns. Although it proved to be difficult to find the
infrared counterpart to this burst, the sub-millimeter flux was relatively
bright. This indicates that intrinsically the brightness of this counterpart
was very similar to GRB 970508. The radio through sub-millimeter spectrum of
GRB 980329 is well fit by a power law with index alpha = +0.9. However, we
cannot exclude a nu^(1/3) power law attenuated by synchrotron self-absorption.
An alpha = +1 VLA-SCUBA power law spectrum is definitely ruled out for GRB
980703, and possibly also for GRB 980519.
  We cannot rule out that part of the sub-millimeter flux from GRB 980329 comes
from a dusty star-forming galaxy at high redshift, such as the ones recently
discovered by SCUBA. Any quiescent dust contribution will be much larger at
sub-millimeter than at radio wavelengths. Both a high redshift and large dust
extinction would help explain the reddening of the counterpart to GRB 980329,
and a redshift of z = 5 has been suggested. The large intensity of this burst
might then indicate that beaming is important.
