Past studies have identified a spatially extended excess of \sim 1-3 GeV gamma rays from the region surrounding the Galactic Center , consistent with the emission expected from annihilating dark matter . We revisit and scrutinize this signal with the intention of further constraining its characteristics and origin . By applying cuts to the Fermi event parameter CTBCORE , we suppress the tails of the point spread function and generate high resolution gamma-ray maps , enabling us to more easily separate the various gamma-ray components . Within these maps , we find the GeV excess to be robust and highly statistically significant , with a spectrum , angular distribution , and overall normalization that is in good agreement with that predicted by simple annihilating dark matter models . For example , the signal is very well fit by a 36-51 GeV dark matter particle annihilating to b \bar { b } with an annihilation cross section of \sigma v = ( 1 - 3 ) \times 10 ^ { -26 } cm ^ { 3 } /s ( normalized to a local dark matter density of 0.4 GeV/cm ^ { 3 } ) . Furthermore , we confirm that the angular distribution of the excess is approximately spherically symmetric and centered around the dynamical center of the Milky Way ( within \sim 0.05 ^ { \circ } of Sgr A ^ { * } ) , showing no sign of elongation along the Galactic Plane . The signal is observed to extend to at least \simeq 10 ^ { \circ } from the Galactic Center , disfavoring the possibility that this emission originates from millisecond pulsars .