For any realistic halo profile, the Galactic Center is predicted to be the brightest source of gammarays from dark matter annihilations. Due in large part to uncertainties associated with the dark matter distribution and astrophysical backgrounds, however, the most commonly applied constraints on the dark matter annihilation cross section have been derived from other regions, such as dwarf spheroidal galaxies. In this article, we study Fermi Gamma-Ray Space Telescope data from the direction of the inner Galaxy and derive stringent upper limits on the dark matter's annihilation cross section. Even for the very conservative case of a dark matter distribution with a significant (∼kpc) constant-density core, normalized to the minimum density needed to accommodate rotation curve and microlensing measurements, we find that the Galactic Center constraint is approximately as stringent as those derived from dwarf galaxies (which were derived under the assumption of an NFW distribution). For NFW or Einasto profiles (again, normalized to the minimum allowed density), the Galactic Center constraints are typically stronger than those from dwarfs.