In merger-driven models of massive galaxy evolution , the luminous quasar phase is expected to be accompanied by vigorous star formation in quasar host galaxies . In this paper , we use high column density Damped Lyman Alpha ( DLA ) systems along quasar sight lines as natural coronagraphs to directly study the far-UV ( FUV ) radiation from the host galaxies of luminous background quasars . We have stacked the spectra of \sim 2,000 DLA systems ( N _ { HI } > 10 ^ { 20.6 } cm ^ { -2 } ) with a median absorption redshift \left \langle z \right \rangle = 2.6 selected from quasars observed in the SDSS-III Baryon Oscillation Spectroscopic Survey . We detect residual flux in the dark troughs of the composite DLA spectra . The level of this residual flux significantly exceeds systematic errors in the SDSS fiber sky subtraction ; furthermore , the residual flux is strongly correlated with the continuum luminosity of the background quasar , while uncorrelated with DLA column density or metallicity . We conclude that the flux could be associated with the average FUV radiation from the background quasar host galaxies ( with medium redshift \left \langle z \right \rangle = 3.1 ) that is not blocked by the intervening DLA . Assuming all of the detected flux originates from quasar hosts , for the highest quasar luminosity bin ( \left \langle L \right \rangle = 2.5 \times 10 ^ { 13 } L _ { \odot } ) , the host galaxy has a FUV intensity of 1.5 \pm 0.2 \times 10 ^ { 40 } erg s ^ { -1 } Å ^ { -1 } ; this corresponds to an unobscured UV star formation rate of 9 M _ { \odot } yr ^ { -1 } .