We report the first high spectral resolution study of 17 M giants kinematically confirmed to lie within a few parsecs of the Galactic center, using R similar to 24,000 spectroscopy from Keck/NIRSPEC and a new line list for the infrared K band. We consider their luminosities and kinematics, which classify these stars as members of the older stellar population and the central cluster. We find a median metallicity of <[Fe H]> = -0.16 and a large spread from approximately -0.3 to +0.3 (quartiles). We find that the highest metallicities are [Fe H] < +0.6, with most of the stars being at or below the solar iron abundance. The abundances and the abundance distribution strongly resemble those of the Galactic bulge rather than the disk or halo; in our small sample we find no statistical evidence for a dependence of velocity dispersion on metallicity.