  We present the significant detection of the first extragalactic pulsar wind
nebula (PWN) detected in gamma rays, N157B, located in the large Magellanic
Cloud (LMC). Pulsars with high spin-down luminosity are found to power
energised nebulae that emit gamma rays up to energies of several tens of TeV.
N157B is associated with PSRJ0537-6910, which is the pulsar with the highest
known spin-down luminosity. The High Energy Stereoscopic System telescope array
observed this nebula on a yearly basis from 2004 to 2009 with a dead-time
corrected exposure of 46 h. The gamma-ray spectrum between 600 GeV and 12 TeV
is well-described by a pure power-law with a photon index of 2.8 \pm 0.2(stat)
\pm 0.3(syst) and a normalisation at 1 TeV of (8.2 \pm 0.8(stat) \pm 2.5(syst))
\times 10^-13 cm^-2s^-1TeV^-1. A leptonic multi-wavelength model shows that an
energy of about 4 \times 10^49erg is stored in electrons and positrons. The
apparent efficiency, which is the ratio of the TeV gamma-ray luminosity to the
pulsar's spindown luminosity, 0.08% \pm 0.01%, is comparable to those of PWNe
found in the Milky Way. The detection of a PWN at such a large distance is
possible due to the pulsar's favourable spin-down luminosity and a bright
infrared photon-field serving as an inverse-Compton-scattering target for
accelerated leptons. By applying a calorimetric technique to these
observations, the pulsar's birth period is estimated to be shorter than 10 ms.
