We report the first results from our program to examine the metallicity distribution of the Milky Way nuclear star cluster connected to Sgr A∗, with the goal of inferring the star formation and enrichment history of this system, as well as its connection and relationship with the central 100 pc of the bulge/bar system. We present the first high-resolution (R ∼ 24,000), detailed abundance analysis of a K = 10.2 metal-poor, alpha-enhanced red giant projected at 1.5 pc from the Galactic center, using NIRSPEC on Keck II. A careful analysis of the dynamics and color of the star locates it at about pc line-of-sight distance in front of the nuclear cluster. It probably belongs to one of the nuclear components (cluster or disk), not to the bar/bulge or classical disk. A detailed spectroscopic synthesis, using a new line list in the K band, finds [Fe/H] ∼ -1.0 and [α/Fe] ∼ 0.4, consistent with stars of similar metallicity in the bulge. As known giants with comparable [Fe/H] and alpha enhancement are old, we conclude that this star is most likely to be a representative of the ∼10 Gyr old population. This is also the most metal-poor-confirmed red giant yet discovered in the vicinity of the nuclear cluster of the Galactic center. We consider recent reports in the literature of a surprisingly large number of metal-poor giants in the Galactic center, but the reported gravity of for these stars calls into question their reported metallicities.