  Recent observations of the Galactic center with ground based gamma-ray
instruments have revealed a TeV (10$^{12}$ eV) gamma-ray signal consistent with
the position of Sgr A*. The derived luminosity of the signal above 1 TeV is a
few $10^{34} \mathrm{erg} \mathrm{s}^{-1}$ which is slightly more than e.g. the
gamma-ray luminosity of the Crab nebula and a plausible identification could be
a conventional albeit strong gamma-ray source. The observations with the
H.E.S.S. system of Cherenkov telescopes have decreased the solid angle
subtended by the error box by more than a factor of hundred with respect to the
previous observations of the VERITAS and CANGAROO groups. After studying the
observed energy spectrum and angular distribution of the excess as seen by the
H.E.S.S. experiment, a massive Dark Matter candidate with a minimum mass of 12
TeV (90 % c.l.) and an upper limit on the WIMP density for $r<10$ pc of $1261
M_\odot \mathrm{pc}^{-3} \times (< \sigma v>/3\cdot10^{-26}
\mathrm{cm}^3\mathrm{s}^{-1})^{-1/2}$ is required to explain the observed flux
by an annihilation signal. The angular distribution of the excess events is
consistent with a cuspy profile with $\rho(r)\propto r^{-\alpha}$ with
$\alpha>1.0$ at a confidence level of 90 %. Even though the mass and the cross
section of the Dark Matter constituents are unexpectedly high in the framework
of most models of nonbaryonic Dark Matter, it can not be ruled out.
