  We present an imaging study of the black hole binary candidate SDSS
J1536+0441 (z=0.3893), based on deep, high resolution VzK images collected at
the ESO/VLT. The images clearly show an asymmetric elongation, indicating the
presence of a companion source at ~1" (~5 kpc projected distance) East from the
quasar. The host galaxy of the quasar is marginally resolved. We find that the
companion source is a luminous galaxy, the light profile of which suggests the
presence of an unresolved, faint nucleus (either an obscured AGN or a compact
stellar bulge). The study of the environment around the quasar indicates the
occurrence of a significant over-density of galaxies with a redshift compatible
with z~0.4. This suggests that it resides in a moderately rich cluster of
galaxies.
