The Vela supernova remnant ( SNR ) is a complex region containing a number of sources of non-thermal radiation . The inner section of this SNR , within 2 degrees of the pulsar \object PSR B0833 - 45 , has been observed by the H .E.S.S . \gamma -ray atmospheric Cherenkov detector in 2004 and 2005 . A strong signal is seen from an extended region to the south of the pulsar , within an integration region of radius 0.8 ^ { \circ } around the position ( \alpha = 08 ^ { h } 35 ^ { m } 00 ^ { s } , \delta = -45 ^ { \circ } 36 \arcmin J2000.0 ) . The excess coincides with a region of hard X-ray emission seen by the ROSAT and ASCA satellites . The observed energy spectrum of the source between 550 GeV and 65 TeV is well fit by a power law function with photon index \Gamma = 1.45 \pm 0.09 _ { \textrm { stat } } \pm 0.2 _ { \textrm { sys } } and an exponential cutoff at an energy of 13.8 \pm 2.3 _ { \textrm { stat } } \pm 4.1 _ { \textrm { sys } } TeV . The integral flux above 1 TeV is ( 1.28 \pm 0.17 _ { \textrm { stat } } \pm 0.38 _ { \textrm { sys } } ) \times 10 ^ { -11 } % \textrm { cm } ^ { -2 } \textrm { s } ^ { -1 } . This result is the first clear measurement of a peak in the spectral energy distribution from a VHE \gamma -ray source , likely related to inverse Compton emission . A fit of an Inverse Compton model to the H .E.S.S . spectral energy distribution gives a total energy in non-thermal electrons of \sim 2 \times 10 ^ { 45 } erg between 5 TeV and 100 TeV , assuming a distance of 290 parsec to the pulsar . The best fit electron power law index is 2.0 , with a spectral break at 67 TeV .