  An annihilation signal of dark matter is searched for from the central region
of the Milky Way. Data acquired in dedicated ON/OFF observations of the
Galactic center region with H.E.S.S. are analyzed for this purpose. No
significant signal is found in a total of $\sim 9$ h of ON/OFF observations.
Upper limits on the velocity averaged cross section, $<\sigma v >$, for the
annihilation of dark matter particles with masses in the range of $\sim 300$
GeV to $\sim 10$ TeV are derived. In contrast to previous constraints derived
from observations of the Galactic center region, the constraints that are
derived here apply also under the assumption of a central core of constant dark
matter density around the center of the Galaxy. Values of $<\sigma v >$ that
are larger than $3\cdot 10^{-24}\:\mathrm{cm^3/s}$ are excluded for dark matter
particles with masses between $\sim 1$ and $\sim 4$ TeV at 95% CL if the radius
of the central dark matter density core does not exceed $500$ pc. This is the
strongest constraint that is derived on $<\sigma v>$ for annihilating TeV mass
dark matter without the assumption of a centrally cusped dark matter density
distribution in the search region.
