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The astrophysical origin of the extended X-ray emission seen in the kiloparsec-scale jets of AGN has been a matter of debate, the two main alternatives being inverse Compton up-scattering of CMB photons by mildly relativistic electrons (of typical Lorentz factors ~ 10^3), or synchrotron emission by ultra-relativistic electrons (of Lorentz factor up to ~ 10^8). In principle, the observation of extended gamma-ray emission, directly probing the presence of ultra-relativistic electrons, could distinguish between these  options. In this talk I will report on the first detection of extended VHE emission in an extragalactic source by H.E.S.S., resolving in-situ particle acceleration to very high energies in the kiloparsec-scale jet of Centaurus A. I will discuss the results and comment on their implications for particle acceleration and TeV emission from AGN.

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