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We present the results of a four-month, spectroscopic campaign of the Wolf-Rayet dust-making binary, WR137. We detect only small-amplitude, random variability in the CIII5696 emission line and its integrated quantities (radial velocity, equivalent width, skewness, kurtosis) that can be explained by stochastic clumps in the wind of the WC star. We find no evidence of large-scale, periodic variations often associated with Corotating Interaction Regions that could have explained the observed intrinsic continuum polarization of this star. Our moderately high-resolution and high signal-to-noise average Keck spectrum shows narrow double-peak emission profiles in the Halpha, Hbeta, Hgamma, HeII6678 and HeII5876 lines. These peaks have a stable blue-to-red intensity ratio with a mean of 0.997 and a root-mean-square of 0.004, commensurate with the noise level; no variability is found during the entire observing period. We suggest that these profiles arise in a decretion disk around the O9 companion, which is thus an O9e star. The characteristics of the profiles are compatible with those of other Be/Oe stars. The presence of this disk can explain the constant component of the continuum polarization of this system, for which the angle is perpendicular to the plane of the orbit, implying that the rotation axis of the O9e star is aligned with that of the orbit. It remains to be explained why the disk is so stable within the strong ultraviolet radiation field of the O star. We present a binary evolutionary scenario that is compatible with the current stellar and system parameters.