The first measurement of the photospheric abundances in a star at the Galactic Center are presented. A detailed abundance analysis of the Galactic Center M2 supergiant IRS 7 was carried out using high-resolution near-infrared echelle spectra. The Fe abundance for IRS 7 was found to be close to solar, [Fe/H] = -0.02 +/- 0.13, and nearly identical to the Fe abundances we obtained for the nearby M supergiants alpha Ori and VV Cep. Analysis of the first and second overtone lines of CO was used to derive an effective temperature of 3600 +/- 230 K, a microturbulent velocity of 3.0 +/- 0.3 km s-1, and a carbon abundance log \epsilon(C) = 7.78 +/- 0.13, or [C/H] = -0.77. In addition, we find a high depletion of 0.74 +/- 0.32 dex in O and an enhancement of 0.92 +/- 0.18 dex in N. These abundances are consistent with the dredge-up of CNO-cycle products but require deep mixing in excess of that predicted by standard models for red supergiants. In light of our measured solar Fe abundance for IRS 7, we discuss other indicators of metallicity at the Galactic Center, the interpretation of low-resolution near-infrared spectra of late-type giants and supergiants, including the need for caution in using such spectra as measures of metallicity, and the evolution of massive young stars at the Galactic Center. We suggest the possibility that rapid stellar rotation is common for stars formed under conditions in the Galactic Center, and that extra internal mixing induced by high rotation rates, rather than evolution at high metallicity, is the explanation for many of the unusual properties of the hot emission-line stars in the Galactic Center.