  The peculiar QSO J0927+2943 shows multiple sets of emission lines in its
optical spectrum. This signature has been interpreted as the relative motion
between a black hole, either recoiling or bound in a binary system, and its
host galaxy, or as a superposition of two galaxies along the line of sight. In
order to test these scenarios, we have collected 2mm CO(2-1) observations using
the IRAM Plateau de Bure Interferometer, and optical images and spectroscopy at
the Calar Alto observatory. Together with archival HST images, these data
provide unique insights on the nature of this system. The recoiling/binary
black hole scenarios are ruled out by the clear detection of a galactic-scale
molecular gas reservoir at the same redshift of the QSO broad lines. The
observations presented here also disfavour the superposition model, although
with less constraints. Thus, the origin of the second, bright set of narrow
emission lines in J0927+2943 is still unknown.
