The advent of sensitive sub-mm array cameras now allows a proper census of dust-enshrouded massive star-formation in very distant galaxies , previously hidden activity to which even the deepest optical images are insensitive . We present the deepest sub-mm survey , taken with the SCUBA camera on the James Clerk Maxwell Telescope ( JCMT ) and centred on the Hubble Deep Field ( HDF ) . The high source density on this image implies that the survey is confusion-limited below a flux density of 2 mJy . However within the central 80 arcsec radius independent analyses yield 5 reproducible sources with S _ { 850 \mu m } > 2 mJy which simulations indicate can be ascribed to individual galaxies . These data lead to integral source counts which are completely inconsistent with a no evolution model , whilst the combined brightness of the 5 most secure sources in our map is sufficient to account for 30–50 % of the previously unresolved sub-mm background , and statistically the entire background is resolved at about the 0.3 mJy level . Four of the five brightest sources appear to be associated with galaxies which lie in the redshift range 2 \leq z < 4 . With the caveat that this is a small sample of sources detected in a small survey area , these submm data imply a star-formation density over this redshift range that is at least five times higher than that inferred from the rest-frame ultraviolet output of HDF galaxies .