In an effort to search for Lyα emission from circum-and intergalactic gas on scales of hundreds of kpc around z ∼ 3 quasar, and thus characterise the physical properties of the gas in emission, we have initiated an extensive fast-survey with the Multi Unit Spectroscopic Explorer (MUSE): Quasar Snapshot Observations with MUse: Search for Extended Ultraviolet eMission (QSO MUSEUM). In this work, we report the discovery of an enormous Lyα nebula (ELAN) around the quasar SDSS J102009.99+104002.7 at z = 3.164, which we followed-up with deeper MUSE observations. This ELAN spans ∼ 297 projected kpc, has an average Lyα surface brightness SB Lyα ∼ 6.04 × 10 −18 erg s −1 cm −2 arcsec −2 (within the 2σ isophote), and is associated with an additional four, previously unknown embedded sources: two Lyα emitters and two faint active galactic nuclei (one Type-1 and one Type-2 quasar). By mapping at high significance the line-of-sight velocity in the entirety of the observed structure, we unveiled a largescale coherent rotation-like pattern spanning ∼ 300 km s −1 with a velocity dispersion of < 270 km s −1 , which we interpret as a signature of the inspiraling accretion of substructures within the quasar's host halo. Future multiwavelength data will complement our MUSE observations, and are definitely needed to fully characterise such a complex system. None the less, our observations reveal the potential of new sensitive integral-field spectrographs to characterise the dynamical state of diffuse gas on large scales in the young Universe, and thereby witness the assembly of galaxies.