We present an elemental-abundance analysis of an extremely metal-poor (EMP; Fe/H <−3.0) star, SDSS J134338.67+484426.6, identified during the course of the Multi-object Apache Point Observatory Radial Velocity Exoplanet Large-area Survey spectroscopic pre-survey of some 20 000 stars to identify suitable candidates for exoplanet searches. This star, with an apparent magnitude V = 12.14, is the lowest metallicity star found in the pre-survey, and is one of only ∼20 known EMP stars that are this bright or brighter. Our high-resolution spectroscopic analysis shows that this star is a subgiant with Fe/H = −3.42, having ‘normal’ carbon and no enhancement of neutron-capture abundances. Strontium is underabundant, Sr/Fe = −0.47, but the derived lower limit on Sr/Ba indicates that Sr is likely enhanced relative to Ba. This star belongs to the sparsely populated class of α-poor EMP stars that exhibit low ratios of Mg/Fe, Si/Fe, and Ca/Fe compared to typical halo stars at similar metallicity. The observed variations in radial velocity from several epochs of (low- and high-resolution) spectroscopic follow-up indicate that SDSS J134338.67+484426.6 is a possible long-period binary. We also discuss the abundance trends in EMP stars for r-process elements, and compare with other magnesium-poor stars.