In 2000, we started the program ``Building the Bridge between Damped Ly-alpha Absorbers and Lyman-Break Galaxies: Ly-alpha Selection of Galaxies at the European Southern Observatorys Very Large Telescope. This project is an attempt to use Ly-alpha selection of high-z galaxies to bridge the gap between absorption- and emission-selected galaxies by creating a large database of z=3 galaxies belonging to the abundant population of faint (R>25.5) galaxies probed by the Damped Ly-alpha Absorbers (DLAs). Here we present the first results of our program, namely the results from a deep Ly-alpha study of the field of the z=2.85 DLA towards Q2138-4427.