The Wolf-Rayet star Mk 34 was observed more than 50 times as part of the deep T-ReX Chandra ACIS-I X-ray imaging survey of the Tarantula Nebula in the Large Magellanic Cloud conducted between 2014 May and 2016 January. Its brightness showed one bright maximum and repeated faint minima which help define an X-ray recurrence time of $155.1pm0.1$ days that is probably the orbital period of an eccentric binary system. The maximum immediately precedes the minimum in the folded X-ray light curve as confirmed by new Swift XRT observations. Notwithstanding its extreme median luminosity of $1.2times10^{35}mathrm{erg}~mathrm{s}^{-1}$, which makes it over an order of magnitude brighter than comparable stars in the Milky Way, Mk 34 is almost certainly a colliding-wind binary system. Its spectrum shows phase-related changes of luminosity and absorption that are probably related to the orbital dynamics of two of the most massive stars known.
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