  The observation of the Egret experiment of an excess of diffuse gamma rays
with energies above E_\gamma =1 GeV has previously been interpreted in the
context of the minimal supergravity model (mSUGRA) as coming from neutralino
annihilation into mainly b-quarks in the galactic halo, with neutralino mass in
the vicinity of 50-70 GeV. We observe that in order to obtain the correct relic
abundance of neutralinos in accord with WMAP measurements, the corresponding
neutralino-proton direct detection (DD) rates should be in excess of recent
limits from the Xenon-10 collaboration. While it does not appear possible to
satisfy the Egret, WMAP and Xenon-10 constraints simultaneously within the
mSUGRA model, we find that it is easily possible in models with non-universal
Higgs soft masses (NUHM). In either case, gluino pair production from
m(gluino)\sim 400-500 GeV should occur at large rates at the CERN LHC, and a
gluino pair production signal should be visible with just 0.1 fb^{-1} of
integrated luminosity. The NUHM interpretation predicts a rather light spectrum
of heavy Higgs bosons with m_A\sim 140-200 GeV over the whole parameter space
which would interpret Egret data. Spin-independent DD rates are predicted to be
just above 10^{-8} pb, within range of the next round of direct dark matter
detection experiments.
