We present the detection of Ly \alpha , [ O iii ] and H \alpha emission associated with an extremely strong damped Lyman- \alpha ( DLA ) system ( N ( { H \textsc { i } } ) = 10 ^ { 22.10 } { cm } ^ { -2 } ) at z = 2.207 towards the quasar SDSS J113520.39 - 001053.56 . This is the largest H i column density ever measured along a QSO line of sight , though typical of what is seen in GRB-DLAs . This absorption system also classifies as ultra-strong Mg ii system with W _ { r } ^ { \lambda 2796 } \simeq 3.6 Å . The mean metallicity of the gas ( [ Zn/H ] = - 1.1 ) and dust depletion factors ( [ Zn/Fe ] = 0.72 , [ Zn/Cr ] = 0.49 ) are consistent with ( and only marginally larger than ) the mean values found in the general QSO-DLA population . The [ O iii ] -H \alpha emitting region has a very small impact parameter with respect to the QSO line of sight , b \approx 0.1 ″ ( 0.9 kpc proper distance ) , and is unresolved . From the H \alpha line , we measure a significant star formation rate SFR \approx 25 M _ { \odot } yr ^ { -1 } ( uncorrected for dust ) . The shape of the Ly \alpha line is double-peaked , which is the signature of resonant scattering of Ly \alpha photons , and the Ly \alpha emission is spatially extended . More strikingly , the blue and red Ly \alpha peaks arise from distinct regions extended over a few kpc on either side of the star-forming region . We propose that this is the consequence of Ly \alpha transfer in outflowing gas . The presence of starburst-driven outflows is also in agreement with the large SFR together with a small size and low mass of the galaxy ( M _ { vir } \sim 10 ^ { 10 } M _ { \odot } ) . From putting constraints on the stellar UV continuum luminosity of the galaxy , we estimate an age of at most a few 10 ^ { 7 } yr , again consistent with a recent starburst scenario . We interpret the data as the observation of a young , gas rich , compact starburst galaxy , from which material is expelled through collimated winds powered by the vigorous star formation activity . We substantiate this picture by modelling the radiative transfer of Ly \alpha photons in the galactic counterpart . Though our model ( a spherical galaxy with bipolar outflowing jets ) is a simplistic representation of the true gas distribution and velocity field , the agreement between the observed and simulated properties is particularly good ( spectral shape and width of the Lyman- \alpha emission , spatial configuration , escape fraction as well as absorption kinematics , H i column density and dust reddening ) . Finally , we propose that selecting DLAs with very high H i column density may be an efficient way to detect star-forming galaxies at small impact parameters from the background QSO lines of sight .