  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 LMg population) has halo-like
kinematics with little to no net rotation. Based on its properties, the origin
of the LMg population is likely as 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 $\it in$ $\it situ$ 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.
