Gamma-ray binaries consist of a neutron star or a black hole interacting with a normal star to produce gamma-ray emission that dominates the radiative output of the system. Only a handful of such systems have been previously discovered, all within our Galaxy. Here we report the discovery with the Fermi Large Area Telescope (LAT) of a luminous gamma-ray binary in the Large Magellanic Cloud from a search for periodic modulation in all sources in the third Fermi LAT catalog. This is the first such system to be found outside the Milky Way. The system has an orbital period of 10.3 days and is associated with a massive O5III star located in the supernova remnant DEM L241, previously identified as the candidate high-mass X-ray binary (HMXB) CXOU J053600.0-673507. X-ray and radio emission are also modulated on the 10.3 day period, but are in anti-phase with the gamma-ray modulation. Optical radial velocity measurements suggest that the system contains a neutron star. The source is significantly more luminous than similar sources in the Milky Way at radio, optical, X-ray and gamma-ray wavelengths. The detection of this extra-galactic system, but no new Galactic systems raises the possibility that the predicted number of gamma-ray binaries in our Galaxy has been overestimated, and that HMXBs may be born containing relatively slowly rotating neutron stars.
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