Deep , 17.8 hours , narrow band imaging obtained at the ESO 3.5m New Technology Telescope has revealed extended ( galaxy sized ) Ly \alpha emission from a high redshift Lyman limit absorber . The absorber is a z _ { abs } \approx z _ { em } Lyman limit absorber seen in the spectrum of Q1205-30 at z _ { em } =3.036 . The Ly \alpha luminosity of the emission line object is 12–14 \times 10 ^ { 41 } h ^ { -2 } erg s ^ { -1 } for \Omega _ { m } =1 . The size and morphology of the Ly \alpha emitter are both near–identical to those of a previously reported emission line object associated with a DLA at z=1.934 ( Fynbo et al . 1999a ) , suggesting a close connection between Lyman limit absorbers and DLAs . We also detect six candidate Ly \alpha emitting galaxies in the surrounding field at projected distances of 156–444h ^ { -1 } kpc with Ly \alpha luminosities ranging from 3.3 to 9.5 \times 10 ^ { 41 } h ^ { -2 } erg s ^ { -1 } for \Omega _ { m } =1 . Assuming no obscuration of Ly \alpha by dust this corresponds to star formation rates in the range 0.3 – 0.9 h ^ { -2 } M _ { \sun } yr ^ { -1 } . Comparing this to the known population of high redshift Lyman break galaxies , we find that the Lyman break galaxies in current ground based samples only make up the very bright end of the high redshift galaxy luminosity function . A significant , and possibly dominating , population of high redshift galaxies are not found in the ground based Lyman break surveys .