  We attempt to build a model that describes the {\it Fermi} galactic gamma-ray
excess (FGCE) within a UV-complete Supersymmetric framework; we find this to be
highly non-trivial. At the very least a successful Supersymmetric explanation
must have several important ingredients in order to fit the data and satisfy
other theoretical and experimental constraints. Under the assumption that a
{\it single} annihilation mediator is responsible for both the observed relic
density as well as the FGCE, we show that the requirements are not easily
satisfied in many TeV-scale SUSY models, but can be met with some model
building effort in the general NMSSM with $\sim 10$ parameters beyond the MSSM.
We find that the data selects a particular region of the parameter space with a
mostly singlino lightest Supersymmetric particle and a relatively light CP-odd
Higgs boson that acts as the mediator for dark matter annihilation. We study
the predictions for various observables within this parameter space, and find
that searches for this light CP-odd state at the LHC, as well as searches for
the direct detection of dark matter, are likely to be quite challenging. It is
possible that a signature could be observed in the flavor sector; however,
indirect detection remains the best probe of this scenario.
