I present observations with the MUSE instrument at the ESO-VLT that reveal the ubiquitous presence of extended Ly-alpha emitting envelopes around individual normal (non-AGN) galaxies at redshifts z > 3. These haloes are larger by factors of ~3-20 than the corresponding rest-frame UV continuum sources as seen by HST. Between ~20% and >~95% of the observed total Ly-alpha flux comes from the extended halo component. At the sensitivity level provided by MUSE, a large fraction of the field of view is actually covered with Ly alpha emission from redshifts 3 < z < 6, and I present a spectacular colour image visualising the "Sky in Ly-alpha". Our observations provide direct insights into the spatial distribution of at least partly neutral gas in the circumgalactic medium of low to intermediate mass galaxies at z > 3. I also discuss some implications for the demographics of high-redshift galaxies.