  BAT99-129 in the LMC is one among a handful of extra-galactic eclipsing
Wolf-Rayet binaries known. We present blue, medium-resolution, phase-dependent
NTT-EMMI spectra of this system that allow us to separate the spectra of the
two components of the binary and to obtain a reliable orbital solution for both
stars. We assign an O5V spectral type to the companion, and WN3(h)a to the
Wolf-Rayet component. We discuss the spectroscopic characteristics of the
system: luminosity ratio, radii, rotation velocities. We find a possible
oversynchronous rotation velocity for the O star. Surprisingly, the extracted
Wolf-Rayet spectrum clearly shows the presence of blueshifted absorption lines,
similar to what has been found in all single hot WN stars in the SMC and some
in the LMC. We also discuss the presence of such intrinsic lines in the context
of hydrogen in SMC and LMC Wolf-Rayet stars, WR+O binary evolution and GRB
progenitors. Altogether, BAT99~129 is the extragalactic counterpart of the
well-known Galactic WR binary V444 Cygni.
