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We report our long-term spectroscopic monitoring of the Pleiades member HII-2147, which has previously been spatially resolved at radio wavelengths in VLBI observations. It has also been claimed to be a (presumably short-period) double-lined spectroscopic binary with relatively sharp lines, although no orbit has ever been published. Examination of our new spectroscopic material, and of the historical radial velocities, shows that the current and previous spectra are best interpreted as showing only a single set of lines of a moderately rapidly rotating star with slowly variable radial velocity, which is one of the sources detected by VLBI. We combine our own and other velocities with the VLBI measurements and new adaptive optics observations to derive the first astrometric-spectroscopic orbit of the G5 + G9 pair, with a period of 18.18 $\pm$ 0.11 years. We infer dynamical masses of 0.897 $\pm$ 0.022 MSun for the spectroscopically visible star and 0.978 $\pm$ 0.024 MSun for the other, along with a distance of 136.78 (+0.50/-0.46) pc. The lack of detection of the lines of the more massive component in our spectra can be adequately explained if it is rotating much more rapidly than the star we see. This is consistent with the observation that the lines of the secondary are shallower than expected for a star of its spectral type.