  We report the results of a spectroscopic and polarimetric study of the
massive, hydrogen-rich WN6h stars R144 (HD 38282 = BAT99-118 = Brey 89) and
R145 (HDE 269928 = BAT99-119 = Brey 90) in the LMC. Both stars have been
suspected to be binaries by previous studies (R144: Schnurr et al. 2008b; R145:
Moffat 1989). We have combined radial-velocity (RV) data from these two studies
with previously unpublished polarimetric data. For R145, we were able to
establish, for the first time, an orbital period of 158.8 days, along with the
full set of orbital parameters, including the inclination angle i, which was
found to be i = 38 \pm 9 deg. By applying a modified version of the
shift-and-add method developed by Demers et al. (2002), we were able to isolate
the spectral signature of the very faint-line companion star. With the RV
amplitudes of both components in R145, we were thus able to estimate their
absolute masses. We find minimum masses M_WR sin^{3}i = (116 \pm 33) M_sol and
M_O sin^{3}i = (48 \pm 20)$ M_sol for the WR and the O component, respectively.
Thus, if the low inclination angle were correct, resulting absolute masses of
the components would be at least 300 and 125 M_sol, respectively. However, such
high masses are not supported by brightness considerations when R145 is
compared to systems with known, very high masses such as NGC3603-A1 or WR20a.
An inclination angle close to 90 degrees would remedy the situation, but is
excluded by the currently available data. More and better data are thus
required to firmly establish the nature of this puzzling, yet potentially very
massive and important system. As to R144, however, the combined data sets are
not sufficient to find any periodicity.
