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 pulsars 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 pulsars 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 pulsars birth period is estimated to be shorter than 10 ms.
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