A deep narrow-band survey for Lyα emission carried out on the VLT-FORS has revealed 98 Lyα candidates down to a flux limit of FLyα ∼ 4 × 10−18 erg s−1 cm−2 in a volume of 5500 comoving Mpc3 at z = 2.4 centred on the hyperluminous quasar HE0109-3518. The properties of the detected sources in terms of their (i) equivalent width distribution, (ii) luminosity function and (iii) the average luminosity versus projected distance from the quasar suggest that a large fraction of these objects have been fluorescently ‘illuminated’ by HE0109-3518. This conclusion is supported by comparison with detailed radiative-transfer simulations of the effects of the quasar illumination. We therefore have a unique opportunity to directly detect and image in emission dense gas, independent of any associated star formation activity. At least 18 objects, a much larger fraction than in ‘blank-field’ Lyα surveys at similar redshifts, have a rest-frame Equivalent Width (EW0) larger than 240 Å, the expected limit for Lyα emission powered by Population II star formation. 12 sources among these do not have any continuum counterpart in a deep V-band imaging of the same field [reaching to V(1σ) ∼ 30.3 AB]. For these, a stacking analysis indicates EW0 > 800 Å (1σ), effectively ruling out Lyα powered by internal star formation. These sources are thus the best candidates so far for proto-galactic clouds or ‘dark’ galaxies at high redshift, whose existence has recently been suggested by several theoretical studies. Assuming they are mostly ionized by the quasar radiation, we estimate that their gas masses would be about Mgas ∼ 109 M⊙, implying that their star formation efficiencies (SFEs) are less than 10−11 yr−1, equivalent to a gas consumption time of 100 Gyr, several times below the average SFE of the most gas-rich dwarf galaxies locally, and 200 times lower than typical massive star-forming galaxies at z ∼ 2. We have also discovered extended, filamentary gas, also likely illuminated by the quasar, around some of the brightest continuum-detected sources with EW0 > 240 Å. The morphology and luminosity of this extended emission are compatible with the expectations for circum-galactic cold streams, as predicted by recent numerical models, but other origins, including tidal stripping, are also possible.