  We report spectropolarimetric observations of the quasar E1821+643 (z=0.297),
which suggest that it may be an example of gravitational recoil due to
anisotropic emission of gravitational waves following the merger of a
supermassive black hole (SMBH) binary. In total flux, the broad Balmer lines
are redshifted by ~1000 km/s relative to the narrow lines and have highly red
asymmetric profiles, whereas in polarized flux the broad H_alpha line exhibits
a blueshift of similar magnitude and a strong blue asymmetry. We show that
these observations are consistent with a scattering model in which the
broad-line region has two components, moving with different bulk velocities
away from the observer and towards a scattering region at rest in the host
galaxy. If the high velocity system is identified as gas bound to the SMBH,
this implies that the SMBH is itself moving with a velocity ~2100 km/s relative
to the host galaxy. We discuss some implications of the recoil hypothesis and
also briefly consider whether our observations can be explained in terms of
scattering of broad-line emission originating from the active component of an
SMBH binary, or from an outflowing wind.
