33 pages, 26 figures, 12 tables and a whole bunch of quasars. Submitted to ApJ ; International audience ; The SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS), a five-year spectroscopic survey of 10,000 deg2, achieved first light in late 2009. One of the key goals of BOSS is to measure the signature of baryon acoustic oscillations (BAOs) in the distribution of Lyα absorption from the spectra of a sample of ~150,000 z > 2.2 quasars. Along with measuring the angular diameter distance at z ≈ 2.5, BOSS will provide the first direct measurement of the expansion rate of the universe at z > 2. One of the biggest challenges in achieving this goal is an efficient target selection algorithm for quasars in the redshift range 2.2 2.20 quasars deg-2). This "CORE" subsample will be fixed for Years Two through Five of the survey. For the remaining 20 targets deg-2, we will continue to develop improved selection techniques, including the use of additional data sets beyond the Sloan Digital Sky Survey (SDSS) imaging data. In this paper, we describe the evolution and implementation of the BOSS QTS algorithms during the first two years of BOSS operations (through 2011 July), in support of the science investigations based on these data, and we analyze the spectra obtained during the first year. During this year, 11,263 new z > 2.20 quasars were spectroscopically confirmed by BOSS, roughly double the number of previously known quasars with z > 2.20. Our current algorithms select an average of 15 z > 2.20 quasars deg-2 from 40 targets deg-2 using single-epoch SDSS imaging. Multi-epoch optical data and data at other wavelengths can further improve the efficiency and completeness of BOSS QTS.