We report the detection of a point-like source of very high energy ( VHE ) \gamma -rays coincident within 1 ^ { \prime } of Sgr A ^ { * } , obtained with the H.E.S.S . array of Cherenkov telescopes . The \gamma -rays exhibit a power-law energy spectrum with a spectral index of -2.2 \pm 0.09 \pm 0.15 and a flux above the 165 GeV threshold of ( 1.82 \pm 0.22 ) \cdot 10 ^ { -7 } m ^ { -2 } s ^ { -1 } . The measured flux and spectrum differ substantially from recent results reported in particular by the CANGAROO collaboration . ;