  We calculate the flux and spectrum of \gamma-rays emitted by a
two-temperature advection-dominated accretion flow (ADAF) around a black hole.
The \gamma-rays are from the decay of neutral pions produced through
proton-proton collisions. We discuss both thermal and power-law distributions
of proton energies and show that the \gamma-ray spectra in the two cases are
very different. We apply the calculations to the \gamma-ray source, 2EG
J1746-2852, detected by EGRET from the direction of the Galactic Center. We
show that the flux and spectrum of this source are consistent with emission
from an ADAF around the supermassive accreting black hole Sgr A^* if the proton
distribution is a power-law. The model uses accretion parameters within the
range made likely by other considerations. If this model is correct, it
provides evidence for the presence of a two temperature plasma in Sgr A^*, and
predicts \gamma-ray fluxes from other accreting black holes which could be
observed with more sensitive detectors.
