We find two chemically distinct populations separated relatively cleanly in the [Fe/H]-[Mg/Fe] plane, but also distinguished in other chemical planes, among metal-poor stars (primarily with metallicities [Fe/H]<-0.9) observed by the Apache Point Observatory Galactic Evolution Experiment (APOGEE) and analyzed for Data Release 13 (DR13) of the Sloan Digital Sky Survey. These two stellar populations show the most significant differences in their [X/Fe] ratios for the {alpha}-elements, C+N, Al, and Ni. In addition to these populations having differing chemistry, the low metallicity high-Mg population (which we denote "the HMg population") exhibits a significant net Galactic rotation, whereas the low-Mg population (or "the LMg population") has halo-like kinematics with little to no net rotation. Based on its properties, the origin of the LMg population is likely an accreted population of stars. The HMg population shows chemistry (and to an extent kinematics) similar to the thick disk, and is likely associated with in situ formation. The distinction between the LMg and HMg populations mimics the differences between the populations of low- and high-{alpha} halo stars found in previous studies, suggesting that these are samples of the same two populations.