We present absolute trigonometric parallaxes and relative proper motions for three members of the Pleiades star cluster, obtained with HST's Fine Guidance Sensor 1r, a white-light interferometer. We estimate spectral types and luminosity classes of the stars comprising the astrometric reference frame from R \approx 2,000 spectra, VJHK photometry, and reduced proper motions. From these we derive estimates of absolute parallaxes and introduce them into our model as observations with error. We constrain the three cluster members to have a 1 sigma dispersion in distance less than 6.4 pc, and find an average pi_{abs}=7.43+-0.17+-0.20 milliseconds of arc, where the second error is systematic due to member placement within the cluster. This parall...