We report the first-ever discovery of a Wolf-Rayet (WR) star in the Large Magellanic Cloud via detection of a circular shell with the Spitzer Space Telescope. Follow-up observations with Gemini-South resolved the central star of the shell into two components separated from each other by a parts per thousand 2 arcsec (or a parts per thousand 0.5 pc in projection). One of these components turns out to be a WN3 star with H and He lines both in emission and absorption (we named it BAT99 3a using the numbering system based on extending the Breysacher et al. catalogue). Spectroscopy of the second component showed that it is a B0 V star. Subsequent spectroscopic observations of BAT99 3a with the du Pont 2.5-m telescope and the Southern African Large Telescope revealed that it is a close, eccentric binary system, and that the absorption lines are associated with an O companion star. We analysed the spectrum of the binary system using the non-LTE Potsdam WR (powr) code, confirming that the WR component is a very hot (a parts per thousand 90 kK) WN star. For this star, we derived a luminosity of log L/ L-aS (TM) = 5.45 and a mass-loss rate of 10(- 5.8) M-aS (TM) yr(- 1), and found that the stellar wind composition is dominated by helium with 20 per cent of hydrogen. Spectroscopy of the shell revealed an He iii region centred on BAT99 3a and having the same angular radius (a parts per thousand 15 arcsec) as the shell. We thereby add a new example to a rare class of high-excitation nebulae photoionized by WR stars. Analysis of the nebular spectrum showed that the shell is composed of unprocessed material, implying that the shell was swept-up from the local interstellar medium. We discuss the physical relationship between the newly identified massive stars and their possible membership of a previously unrecognized star cluster.