摘要:Context.Recently, the high-energy (HE, 0.1–100 GeV)γ-ray emission from the object LMC P3 in the Large Magellanic Cloud (LMC) has been discovered to be modulated with a 10.3-day period, making it the first extra-galacticγ-ray binary.Aim.This work aims at the detection of very-high-energy (VHE, >100 GeV)γ-ray emission and the search for modulation of the VHE signal with the orbital period of the binary system.Methods.LMC P3 has been observed with the High Energy Stereoscopic System (H.E.S.S.); the acceptance-corrected exposure time is 100 h. The data set has been folded with the known orbital period of the system in order to test for variability of the emission.Results.VHEγ-ray emission is detected with a statistical significance of 6.4σ. The data clearly show variability which is phase-locked to the orbital period of the system. Periodicity cannot be deduced from the H.E.S.S. data set alone. The orbit-averaged luminosity in the 1–10 TeV energy range is (1.4 ± 0.2) × 1035 erg s−1. A luminosity of (5 ± 1) × 1035 erg s−1is reached during 20% of the orbit. HE and VHEγ-ray emissions are anti-correlated. LMC P3 is the most luminousγ-ray binary known so far.