The Apache Point Observatory Galactic Evolution Experiment (APOGEE), part of the Sloan Digital Sky Survey III, is exploring the stellar populations of the Milky Way using the Sloan 2.5-m telescope linked to a high resolution (R 22,500), near-infrared (1.51-1.68 microns) spectrograph with 300 optical fibers. For about 100,000, predominantly red giant branch stars that APOGEE is targeting across the Galactic bulge, disks and halo, the collected high S/N (>100 per Nyquist-limit-sized pixel) spectra will provide accurate (+/-200 m/s) radial velocities, stellar atmospheric parameters, and precise (+/- 0.1 dex) chemical abundances for about 15 chemical species. The APOGEE survey targeting plan includes fields that have been specifically placed on either the core or tails of the Sagittarius (Sgr) dSph galaxy. Some of the target selection has relied on known or suspected giant star members of Sgr identified in previous surveys. But other fields in the path of the Sgr stream serendipitously uncover additional Sgr stars through the normal APOGEE giant star targeting. We report on early results from APOGEE commissioning data that include dozens of Sgr stars spread over several distinct pointings on the Sgr core. In addition, we report the discovery of Sgr stars found in several pointings directed at the Galactic bulge and midplane. These data for Sgr stars lying behind some of the dustiest parts of the Milky Way yield accurate velocities, velocity dispersions and chemical information on stretches of the Sagittarius stream never before explored. The results can be used to refine models of the chemodynamical evolution of the Sgr system and the shape of the gravitational potential of the Milky Way.