We report the detection of TeV \gamma -rays from the shell-type supernova remnant RX J0852.0 $ - $ 4622 with data of 3.2 h of live time recorded with H.E.S.S . in February 2004 . An excess of ( 700 \pm 60 ) events from the whole remnant with a significance of 12 \sigma was found . The observed emission region is clearly extended with a radius of the order of 1 \degr and the spatial distribution of the signal correlates with X-ray observations . The spectrum in the energy range between 500 GeV and 15 TeV is well described by a power law with a photon index of \Gamma = 2.1 \pm 0.1 _ { \mathrm { stat } } \pm 0.2 _ { \mathrm { syst } } and a differential flux at 1 TeV of \varphi _ { 1 \mathrm { TeV } } = ( 2.1 \pm 0.2 _ { \mathrm { stat } } \pm 0.6 _ { \mathrm { syst } } ) % \times 10 ^ { -11 } \mbox { cm } ^ { -2 } \mbox { s } ^ { -1 } \mbox { TeV } ^ { -1 } . The integral flux above 1 TeV was measured to be \Phi ( E > 1 \mbox { TeV } ) = ( 1.9 \pm 0.3 _ { \mathrm { stat } } \pm 0.6 _ { \mathrm { syst } } ) % \times 10 ^ { -11 } \mbox { cm } ^ { -2 } \mbox { s } ^ { -1 } , which is at the level of the flux of the Crab nebula at these energies . More data are needed to draw firm conclusions on the magnetic field in the remnant and the type of the particle population creating the TeV \gamma -rays .