  Recent analysis of data sets from two extensive air shower cosmic ray
detectors shows tantalizing evidence of an anisotropic overabundance of cosmic
rays towards the Galactic Center (GC) that ``turns on'' around $10^{18}$ eV. We
demonstrate that the anisotropy could be due to neutrons created at the
Galactic Center through charge-exchange in proton-proton collisions, where the
incident, high energy protons obey an $\sim E^{-2}$ power law associated with
acceleration at a strong shock. We show that the normalization supplied by the
gamma-ray signal from EGRET GC source 3EG J1746-2851 -- ascribed to pp induced
neutral pion decay at GeV energies -- together with a very reasonable spectral
index of 2.2, predicts a neutron flux at $\sim 10^{18}$ eV fully consistent
with the extremely high energy cosmic ray data. Likewise, the normalization
supplied by the very recent GC data from the HESS air-Cerenkov telescope at
\~TeV energies is almost equally-well compatible with the $\sim 10^{18}$ eV
cosmic ray data. Interestingly, however, the EGRET and HESS data appear to be
themselves incompatible. We consider the implications of this discrepancy. We
discuss why the Galactic Center environment can allow diffusive shock
acceleration at strong shocks up to energies approaching the ankle in the
cosmic ray spectrum. Finally, we argue that the shock acceleration may be
occuring in the shell of Sagittarius A East, an unusual supernova remnant
located very close to the Galactic Center. If this connection between the
anisotropy and Sagittarius A East could be firmly established it would be the
first direct evidence for a particular Galactic source of cosmic rays up to
energies near the ankle.
