We report on the search for galaxies in the proximity of two very metal-poor gas clouds at z \sim 3 towards the quasar Q0956 + 122 . With a 5-hour MUSE integration in a \sim 500 \times 500 kpc ^ { 2 } region centred at the quasar position , we achieve a \geq 80 \% complete spectroscopic survey of continuum-detected galaxies with m _ { R } \leq 25 mag and Ly \alpha emitters with luminosity L _ { Ly \alpha } \geq 3 \times 10 ^ { 41 } ~ { } erg~ { } s ^ { -1 } . We do not identify galaxies at the redshift of a z \sim 3.2 Lyman limit system ( LLS ) with \log Z / Z _ { \odot } = -3.35 \pm 0.05 , placing this gas cloud in the intergalactic medium or circumgalactic medium of a galaxy below our sensitivity limits . Conversely , we detect five Ly \alpha emitters at the redshift of a pristine z \sim 3.1 LLS with \log Z / Z _ { \odot } \leq - 3.8 , while \sim 0.4 sources were expected given the z \sim 3 Ly \alpha luminosity function . Both this high detection rate and the fact that at least three emitters appear aligned in projection with the LLS suggest that this pristine cloud is tracing a gas filament that is feeding one or multiple galaxies . Our observations uncover two different environments for metal-poor LLSs , implying a complex link between these absorbers and galaxy halos , which ongoing MUSE surveys will soon explore in detail . Moreover , in agreement with recent MUSE observations , we detected a \sim 90 ~ { } kpc Ly \alpha nebula at the quasar redshift and three Ly \alpha emitters reminiscent of a “ dark galaxy ” population .