We present new observations acquired with the Multi Unit Spectroscopic Explorer instrument on the Very Large Telescope in a quasar field that hosts a high column-density damped Ly \alpha absorber ( DLA ) at z \approx 3.25 . We detect Ly \alpha emission from a nebula at the redshift of the DLA with line luminosity ( 27 \pm 1 ) \times 10 ^ { 41 } ~ { } erg~ { } s ^ { -1 } , which extends over 37 \pm 1 ~ { } kpc above a surface brightness limit of 6 \times 10 ^ { -19 } ~ { } erg~ { } s ^ { -1 } ~ { } cm ^ { -2 } ~ { } arcsec ^ { -2 } at a projected distance of 30.5 \pm 0.5 ~ { } kpc from the quasar sightline . Two clumps lie inside this nebula , both with Ly \alpha rest-frame equivalent width > 50 ~ { } \AA and with relative line-of-sight velocities aligned with two main absorption components seen in the DLA spectrum . In addition , we identify a compact galaxy at a projected distance of 19.1 \pm 0.5 ~ { } kpc from the quasar sightline . The galaxy spectrum is noisy but consistent with that of a star-forming galaxy at the DLA redshift . We argue that the Ly \alpha nebula is ionized by radiation from star formation inside the two clumps , or by radiation from the compact galaxy . In either case , these data imply the presence of a structure with size \gg 50 kpc inside which galaxies are assembling , a picture consistent with galaxy formation in groups and filaments as predicted by cosmological simulations such as the eagle simulations .