We present the significant detection of the first extragalactic pulsar wind nebula ( PWN ) detected in gamma rays , N 157B , 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 . N 157B is associated with PSR J0537 - 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 _ { \mathrm { stat } } \pm 0.3 _ { \mathrm { syst } } and a normalisation at 1 TeV of ( 8.2 \pm 0.8 _ { \mathrm { stat } } \pm 2.5 _ { \mathrm { syst } } ) \times 10 ^ { -13 } \mathrm { cm% } ^ { -2 } \mathrm { s } ^ { -1 } \mathrm { TeV } ^ { -1 } . A leptonic multi-wavelength model shows that an energy of about 4 \times 10 ^ { 49 } \mathrm { erg } is stored in electrons and positrons . The apparent efficiency , which is the ratio of the TeV gamma-ray luminosity to the pulsar ’ s spin-down 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 .