  We discuss our ongoing program of Target of Opportunity (ToO) sub-millimeter
observations of gamma-ray bursts (GRBs) using the Sub-millimetre Common-User
Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope (JCMT). In this
paper, we present all the ToO observations of GRB 030329. This was by far the
brightest sub-millimeter afterglow seen to date. The flux density at 850
microns was approximately constant up to a break that took place ~7 days after
the burst. This was consistent with being a jet break. The 850 micron results
agree with those at longer wavelengths that show a brighter flux ~7 days after
the burst, right at the time of the break. No short-lived large-scale
brightenings were detected in the sub-millimeter light curve. However, the 850
micron light curve may have had a drop <~ 16 days after the burst. The peak of
the afterglow emission was at ~90 GHz in the days before the break in the light
curve. A simple modeling is consistent with the spectral indices remaining the
same as the afterglow evolved, with the breaks in the spectrum moving to longer
wavelengths at later times and the flux at the peak falling. No significant
sub-millimeter emission was detected from the host galaxy.
