  We report the discovery of extremely broad 21-cm HI absorption (FWZI ~1600
km/s) detected with the Westerbork Synthesis Radio Telescope in the radio
source 4C37.11 (B2 0402+379). This object has been claimed to host a
super-massive binary black hole (Rodriguez et al. 2006). The main features in
the absorption profile are two components, separated by ~1100 km/s. The HI
absorption in 4C37.11 is unusual because it is the first case where such broad
absorption is found to be centred on the systemic velocity of the host galaxy
and not asymmetric and blueshifted as is seen in all other galaxies with broad
HI absorption. Given the large width of the absorption, we suggest that a
possible explanation for the extreme properties of the HI absorption is that it
is the kinematic signature of a binary black hole. If this interpretation is
correct, the combined black hole mass derived from the absorption profile is
consistent with that derived from the luminosity of the spheroid. If the broad
absorption is indeed due to a binary black hole, this finding confirms the
importance of the gaseous component in the merging process of supermassive
black holes.
