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We utilize the Multi Unit Spectroscopic Explorer (MUSE) on the Very LargeTelescope (VLT) to search for extended Lyman-Alpha emission around the z~6.6QSO J0305-3150. After carefully subtracting the point-spread-function, we reacha 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 wavelengthslices centered at the expected location of the redshifted Lyman-Alpha emission(i.e. at 9256 Ang.). Current data suggest the presence (5-sigma, accounting forsystematics) 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 thelocation of the QSO host galaxy traced by the [CII] emission line. The totalluminosity is L = 3.0x10$^{42}$ erg/s. Our analysis suggests that this emissionis unlikely to rise from optically thick clouds illuminated by the ionizingradiation of the QSO. It is more plausible that the Lyman-Alpha emission is dueto fluorescence of the highly ionized optically thin gas. This scenario impliesa high hydrogen volume density of n$_H$ ~ 6 cm$^{-3}$. In addition, we detect aLyman-Alpha emitter (LAE) in the immediate vicinity of the QSO: i.e., with aprojected separation of 12.5 kpc and a line-of-sight velocity difference of 560km/s. The luminosity of the LAE is L = 2.1x10$^{42}$ erg/s and its inferredstar-formation-rate is SFR ~ 1.3 M$_\odot$/yr. The probability of finding sucha close LAE is one order of magnitude above the expectations based on theQSO-galaxy cross-correlation function. This discovery is in agreement with ascenario where dissipative interactions favour the rapid build-up ofsuper-massive black holes at early Cosmic times.

Mapping the Lyman-Alpha Emission Around a z~6.6 QSO with MUSE: Extended Emission and a Companion at Close Separation