  Despite extensive observational efforts, the brightest sub--mm source in the
Hubble Deep Field, HDF850.1, has failed to yield a convincing optical/infrared
identification almost 4 years after its discovery. This failure is all the more
notable given the availability of supporting multi-frequency data of
unparalleled depth, and sub-arcsec positional accuracy for the sub-mm/mm
source. Consequently, HDF850.1 has become a test case of the possibility that
the most violently star-forming objects in the universe are too red and/or
distant to be seen in the deepest optical images. Here we report the discovery
of the host galaxy of HDF850.1. This object has been revealed by careful
analysis of a new, deep K-prime image of the HDF obtained with the Subaru 8.2-m
telescope. Its reality is confirmed by a similar analysis of the HST NICMOS
F160W image of the same region. This object is extremely faint (K=23.5), clumpy
(on sub-arcsec scales) and very red (I-K > 5.2; H-K = 1.4 +- 0.35). The
likelihood that it is the correct identification is strongly reinforced by a
reanalysis of the combined MERLIN+VLA 1.4-GHz map of the field which yields a
new radio detection of HDF850.1 only 0.1 arcsec from the new near-ir
counterpart, and with sufficient positional accuracy to exclude all previously
considered alternative optical candidates. We have calculated new confidence
limits on the estimated redshift of HDF850.1 and find z = 4.1 +- 0.5. We also
calculate that the flux density of HDF850.1 has been boosted by a factor of ~3
through lensing by the intervening elliptical 3-586.0, consistent with
predictions that a small but significant fraction of blank-field sub-mm sources
are lensed by foreground galaxies. We discuss the wider implications of these
results for the sub-mm population and cosmic star-formation history.
