We show that the position of the central dark matter (DM) density peak may be expected to differ from the dynamical center of the Galaxy by several hundred parsecs. In Eris, a high-resolution cosmological hydrodynamics simulation of a realistic Milky-Way-analog disk galaxy, this offset is 300-400 pc (~3 gravitational softening lengths) after z = 1. In its dissipationless DM-only twin simulation ErisDark, as well as in the Via Lactea II and GHalo simulations, the offset remains below one softening length for most of its evolution. The growth of the DM offset coincides with a flattening of the central DM density profile in Eris inward of ~1 kpc, and the direction from the dynamical center to the point of maximum DM density is correlated with the orientation of the stellar bar, suggesting a bar-halo interaction as a possible explanation. A DM density offset of several hundred parsecs greatly affects expectations of the DM annihilation signals from the Galactic center. It may also support a DM annihilation interpretation of recent reports by Weniger and Su & Finkbeiner of highly significant 130 GeV gamma-ray line emission from a region 1.°5 (~200 pc projected) away from Sgr A* in the Galactic plane.