  VFTS 682 is located in an active star-forming region, at a projected distance
of 29 pc from the young massive cluster R136 in the Tarantula Nebula of the
Large Magellanic Cloud. It was previously reported as a candidate young stellar
object, and more recently spectroscopically revealed as a hydrogen-rich
Wolf-Rayet (WN5h) star. Our aim is to obtain the stellar properties, such as
its intrinsic luminosity, and to investigate the origin of VFTS 682. To this
purpose, we model optical spectra from the VLT-FLAMES Tarantula Survey with the
non-LTE stellar atmosphere code CMFGEN, as well as the spectral energy
distribution from complementary optical and infrared photometry. We find the
extinction properties to be highly peculiar (RV ~4.7), and obtain a
surprisingly high luminosity log(L/Lsun) = 6.5 \pm 0.2, corresponding to a
present-day mass of ~150Msun. The high effective temperature of 52.2 \pm 2.5kK
might be explained by chemically homogeneous evolution - suggested to be the
key process in the path towards long gamma-ray bursts. Lightcurves of the
object show variability at the 10% level on a timescale of years. Such changes
are unprecedented for classical Wolf-Rayet stars, and are more reminiscent of
Luminous Blue Variables. Finally, we discuss two possibilities for the origin
of VFTS 682: (i) the star either formed in situ, which would have profound
implications for the formation mechanism of massive stars, or (ii) VFTS 682 is
a slow runaway star that originated from the dense cluster R136, which would
make it the most massive runaway known to date.
