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 and 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 6 x 3 arcsec(2), corresponding to 25 x 12 h(-2) kpc(2) (q(0) = 0.5, H(0) = 100 h km s(-1)). The total Ly alpha luminosity from the DLA is 1.2 x 10(43) h(-2) erg s(-1), which is several times 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 similar to 300 km s(-1) blueshift relative to the DLA, can plausibly be explained if qB is the source of ionizing 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 discs 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 hat, and we would expect that some 70 per cent of the galaxy counterparts to DLAs at z approximate to 3 are fainter than m(R) = 28.