The number of damped Ly \alpha absorbers ( DLAs ) currently known is about 100 , but our knowledge of their sizes and morphologies is still very sparse as very few have been detected in emission . Here we present narrow–band and broad–band observations of a DLA in the field of the quasar pair Q0151+048A ( qA ) and Q0151+048B ( qB ) . These two quasars have very similar redshifts z _ { em } =1.922 , 1.937 , respectively , and an angular separation of 3.27 arcsec . The spectrum of qA contains a DLA at z _ { abs } = 1.9342 ( close to the emission redshift ) which shows an emission line in the trough , detected at 4 \sigma . Our narrow–band image confirms this detection and we find Ly \alpha emission from an extended area covering 6x3 arcsec ^ { 2 } , corresponding to 25x12h ^ { -2 } kpc ^ { 2 } ( q _ { 0 } =0.5 , H _ { 0 } = 100h km s ^ { -1 } ) . The total Ly \alpha luminosity from the DLA is 1.2 x 10 ^ { 43 } h ^ { -2 } erg s ^ { -1 } , which is a factor of several higher than the Ly \alpha luminosity found from other DLAs . The narrow–band image also indicates that qB is not covered by the DLA . This fact , together with the large equivalent width of the emission line from the Ly \alpha cloud , the large luminosity , and the \sim 300 km s ^ { -1 } blueshift relative to the DLA , can plausibly be explained if qB is the source of ionising photons , lying to the near side of the DLA at a distance from the DLA of < 20 h ^ { -1 } kpc . In this case the size of the emission-line region corresponds to the area over which the cloud is optically thick , i.e . is indicative of the size of a Lyman-limit system . We also consider the relation between DLAs and Lyman-break galaxies ( LBGs ) . If DLAs are gaseous disks surrounding LBGs , and if the apparent brightnesses and impact parameters of the few identified DLAs are representative of the brighter members of the population , then the luminosity distribution of DLAs is nearly flat , and we would expect that some 70 \% of the galaxy counterparts to DLAs at z \approx 3 are fainter than m _ { R } = 28 .