We have used the Submillimeter Common-User Bolometer Array (SCUBA) detector
on the James Clerk Maxwell Telescope to measure bright submillimeter emiss
ion associated with a recently discovered extensive (>100 h(-1) kpc) and hi
ghly luminous "blob" of Ly alpha emission at z = 3.09. The blob lies within
a known large overdensity of optical sources in the z = 3.07-3.11 range an
d is centered on a locally overdense peak within this region. The best expl
anation for the copious submillimeter emission is a dust-obscured continuum
source, which may produce the ionizing flux for the Ly alpha cloud. Coolin
g gas explanations are plausible but excessively complicated, and the 450/8
50 mum ratio rules out a significant fraction of the signal arising from th
e Sunyaev-Zeldovich increment. At least two additional similar or equal to
10 mJy submillimeter detections in the SCUBA map, with a surface density si
gnificantly higher than in blank-field surveys, suggest that they may be as
sociated with the z = 3.09 structure. A SCUBA "photometry" observation of a
second nearby Ly alpha blob tentatively detects a weaker submillimeter cou
nterpart.