Recently, the $gamma$-ray emission at MeV and GeV energies from the object LMC P3 in the Large Magellanic Cloud has been discovered to be modulated with a 10.3-days period, making it the first extra-galactic $gamma$-ray binary. This work aims at the detection of TeV $gamma$-ray and the search for modulation of the signal with the orbital period of the binary system. The H.E.S.S. data set has been folded with the known orbital period of the system in order to test for variability of the emission. Energy spectra are obtained for the orbit-averaged data set and for orbital phases in which the TeV flux is found at its maximum. TeV $gamma$-ray emission is detected with a statistical significance of 6.4,$sigma$. 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 $(1.4 pm 0.2) times 10^{35},mathrm{erg,s}^{-1}$. A luminosity of $(5 pm 1) times 10^{35},mathrm{erg,s}^{-1}$ is reached during 20% of the orbit, when the MeV/GeV emission is at its minimum.
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