We report the detection of a point-like source of very high energy (VHE) γ-rays coincident within 1' of Sgr A*, obtained with the HESS array of Cherenkov telescopes. The γ-rays exhibit a power-law energy spectrum with a spectral index of -2.2 ± 0.09 ± 0.15 and a flux above the 165 GeV threshold of (1.82 ± 0.22) × 10-7 m-2 s-1. The measured flux and spectrum differ substantially from recent results reported in particular by the CANGAROO collaboration.