The inner region of the Milky Way halo harbors a large amount of dark matter ( DM ) .
Given its proximity , it is one of the most promising targets to look for DM .
We report on a search for the annihilations of DM particles using \gamma -ray observations towards the inner 300 parsecs of the Milky Way , with the H.E.S.S .
array of ground-based Cherenkov telescopes .
The analysis is based on a 2D maximum likelihood method using Galactic center ( GC ) data accumulated by H.E.S.S .
over the last 10 years ( 2004-2014 ) , and does not show any significant \gamma -ray signal above background .
Assuming Einasto and Navarro-Frenk-White DM density profiles at the GC , we derive upper limits on the annihilation cross section \langle \sigma v \rangle .
These constraints are the strongest obtained so far in the TeV DM mass range and improve upon previous limits by a factor 5 .
For the Einasto profile , the constraints reach \langle \sigma v \rangle values of 6 \times 10 ^ { -26 } cm ^ { 3 } s ^ { -1 } in the W ^ { + } W ^ { - } channel for a DM particle mass of 1.5 TeV , and 2 \times 10 ^ { -26 } cm ^ { 3 } s ^ { -1 } in the \tau ^ { + } \tau ^ { - } channel for 1 TeV mass .
For the first time , ground-based \gamma -ray observations have reached sufficient sensitivity to probe \langle \sigma v \rangle values expected from the thermal relic density for TeV DM particles .