In 2000, we started the program "Building the Bridge between Damped Lyman-α Absorbers and Lyman-Break Galaxies: Lyα Selection of Galaxies" at the European Southern Observatory's Very Large Telescope (VLT). This project is an attempt to use the Lyα selection of high-redshift galaxies to bridge the gap between absorption- and emission-line selected galaxies by creating a large database of z ≈ 3 galaxies belonging to the abundant population of faint (R > 25:5) galaxies associated to Damped Lyα Absorbers (DLAs). Here we present the first part of our program, namely results from a deep Lyα study of the field of the z = 2:85 DLA toward the quasar Q2138-4427.