  We present optical and near-infrared observations with Keck of the binary
millisecond pulsar PSR J0751+1807. We detect a faint, red object - with
R=25.08+-0.07, B-R=2.5+-0.3, and R-I=0.90+-0.10 - at the celestial position of
the pulsar and argue that it is the white dwarf companion of the pulsar. The
colours are the reddest among all known white dwarfs, and indicate a very low
temperature, Teff~4000 K. This implies that the white dwarf cannot have the
relatively thick hydrogen envelope that is expected on evolutionary grounds.
Our observations pose two puzzles. First, while the atmosphere was expected to
be pure hydrogen, the colours are inconsistent with this composition. Second,
given the low temperature, irradiation by the pulsar should be important, but
we see no evidence for it. We discuss possible solutions to these puzzles.
