  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 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 deg. around the position (RA = 08h 35m 00s, dec = -45 deg. 36'
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 = 1.45
+/- 0.09(stat) +/- 0.2(sys) and an exponential cutoff at an energy of 13.8 +/-
2.3(stat) +/- 4.1(sys) TeV. The integral flux above 1 TeV is (1.28 +/- 0.17
(stat) +/- 0.38(sys)) x 10^{-11} cm^{-2} 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 ~2 x 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.
