Galaxies are surrounded by large reservoirs of gas, mostly hydrogen, fed by inflows from the intergalactic medium and by outflows due to galactic winds. Absorption-line measurements along the sightlines to bright and rare background quasars indicate that this circumgalactic medium pervades far beyond the extent of starlight in galaxies, but very little is known about the spatial distribution of this gas. A new window into circumgalactic environments was recently opened with the discovery of ubiquitous extended Lyman-α emission from hydrogen
around high-redshift galaxies, facilitated by the extraordinary sensitivity of the MUSE instrument at the ESO Very Large Telescope. Due to the faintness of this emission, such measurements were previously limited to especially favourable systems or to massive statistical averaging. Here we demonstrate that low surface brightness Lyman-α emission surrounding faint galaxies at redshifts between 3 and 6 adds up to a projected sky coverage of nearly 100%. The corresponding rate of incidence (the mean number of Lymanα emitters penetrated by any arbitrary line of sight) is well above unity and similar to the incidence rate of high column density absorbers frequently detected in the spectra of distant quasars. This similarity suggests that most circumgalactic atomic hydrogen at these redshifts has now been detected also in emission