We searched quasar spectra from the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) for the rare occurrences where a strong damped Lyman-alpha absorber (DLA) blocks the Broad Line Region emission from the quasar and acts as a natural coronagraph to reveal narrow Lyalpha emission from the host galaxy. We define a statistical sample of 31 DLAs in Data Release 9 (DR9) with log N(HI) > 21.3 cm^-2 located at less than 1500 km s^-1 from the quasar redshift. In 25% (8) of these DLAs, a strong narrow Lyalpha emission line is observed with flux ~25 x 10^-17 erg s^-1 cm^-2 on average. For DLAs without this feature in their troughs, the average 3-sigma upper limit is < 0.8 x 10^-17 erg s^-1 cm^-2. Our statistical sample is nearly 2.5 times larger than the anticipated number of intervening DLAs in DR9 within 1500 km s^-1 of the quasar redshift. We also define a sample of 26 DLAs from DR9 and DR10 with narrow Lyalpha emission detected and no limit on the HI column density to better characterize properties of the host galaxy emission. Analyzing the statistical sample, we do not find substantial differences in the kinematics, metals, or reddening for the two populations with and without emission detected. The highly symmetric narrow Lyalpha emission line profile centered in the HI trough indicates that the emitting region is separate from the absorber. The luminosity of the narrow Lyalpha emission peaks is intermediate between that of Lyman-alpha emitters and radio galaxies, implying that the Lyalpha emission is predominantly due to ionizing radiation from the AGN. Galaxies neighboring the quasar host are likely responsible for the majority (> 75%) of these DLAs, with only a minority (< 25%) arising from HI clouds located in the AGN host galaxy.
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