  T and Y-dwarfs are among the coolest and least luminous objects detected, and
they can help to understand the properties of giant planets. Their multiplicity
properties can shed light on the formation process. We observed a sample six T
dwarfs and one L9 dwarf with the Laser Guide Star (LGS) and NAOS-CONICA, the
adaptive optics (AO) facility, and the near infrared camera at the ESO Very
Large Telescope. From the seven observed objects, we have identified a
subarcsecond binary system, WISE J0612-3036, composed of two similar components
with spectral types of T6. We measure a separation of $\rho$ = 350$\pm$5 mas
and a position angle of $PA = 235\pm1^{\circ}$. Using the mean absolute
magnitudes of T6 dwarfs in the 2MASS $JHK_s$ bands, we estimate a distance of
$d$=31$\pm$6 pc and derive a projected separation of $\rho$ = 11$\pm$2 au.
Another target, WISE J2255-3118, shows a very faint object at 1.3 arcsec in the
$K_{\rm s}$ image. The object is marginally detected in $H$, and we derive a
near infrared color of $H-K_{\rm s}$$>$ 0.1\,mag. $HST/WFC3$ public archival
data reveals that the companion candidate is an extended source.Together with
the derived color, this suggests that the source is most probably a background
galaxy. The five other sources are apparently single, with 3-$\sigma$
sensitivity limits between $H$=19-21 for companions at separations $\geq$ 0.5
arcsec. WISE 0612-3036 is probably a new T-dwarf binary composed of two T6
dwarfs. As in the case of other late T-dwarf binaries, it shows a mass ratio
close to 1, although its projected separation, $\sim$11 au, is larger than the
average ($\sim$ 5 au). Additional observations are needed to confirm that the
system is bound.
