We report the discovery of 13 confirmed two-image quasar lenses from a systematic search for gravitationally lensed quasars in the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS). We adopted a methodology similar to that used in the SDSS Quasar Lens Search (SQLS). In addition to the confirmed lenses, we report 11 quasar pairs with small angular separations ( ≲ 2 arcsec) confirmed from our spectroscopy, which are either projected pairs, physical binaries, or possibly quasar lens systems whose lens galaxies have not yet been detected. The newly discovered quasar lens system, SDSS J1452+4224 at zs ≈ 4.8 is one of the highest redshift multiply imaged quasars found to date. Furthermore, we have over 50 good lens candidates yet to be followed up. Owing to the heterogeneous selection of BOSS quasars, the lens sample presented here does not have a well-defined selection function.