  We utilize the Multi Unit Spectroscopic Explorer (MUSE) on the Very Large
Telescope (VLT) to search for extended Lyman-Alpha emission around the z~6.6
QSO J0305-3150. After carefully subtracting the point-spread-function, we reach
a nominal 5-sigma surface brightness limit of SB = 1.9x10$^{-18}$
erg/s/cm$^2$/arcsec$^2$ over a 1 arcsec$^2$ aperture, collapsing 5 wavelength
slices centered at the expected location of the redshifted Lyman-Alpha emission
(i.e. at 9256 Ang.). Current data suggest the presence (5-sigma, accounting for
systematics) of a Lyman-Alpha nebula that extends for 9 kpc around the QSO.
This emission is displaced and redshifted by 155 km/s with respect to the
location of the QSO host galaxy traced by the [CII] emission line. The total
luminosity is L = 3.0x10$^{42}$ erg/s. Our analysis suggests that this emission
is unlikely to rise from optically thick clouds illuminated by the ionizing
radiation of the QSO. It is more plausible that the Lyman-Alpha emission is due
to fluorescence of the highly ionized optically thin gas. This scenario implies
a high hydrogen volume density of n$_H$ ~ 6 cm$^{-3}$. In addition, we detect a
Lyman-Alpha emitter (LAE) in the immediate vicinity of the QSO: i.e., with a
projected separation of 12.5 kpc and a line-of-sight velocity difference of 560
km/s. The luminosity of the LAE is L = 2.1x10$^{42}$ erg/s and its inferred
star-formation-rate is SFR ~ 1.3 M$_\odot$/yr. The probability of finding such
a close LAE is one order of magnitude above the expectations based on the
QSO-galaxy cross-correlation function. This discovery is in agreement with a
scenario where dissipative interactions favour the rapid build-up of
super-massive black holes at early Cosmic times.
