  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 parallax
corresponds to a distance of 134.6+-3.1 pc or a distance modulus of
(m-M)=5.65+-0.05 for these three Pleiads, presuming a central location. This
result agrees with three other independent determinations of the Pleiades
distance. Presuming that the cluster depth systematic error can be
significantly reduced because of the random placement of these many members
within the cluster, these four independent measures yield a best-estimate
Pleiades distance of pi_{abs}=7.49+-0.07 milliseconds of arc, corresponding to
a distance of 133.5+-1.2 pc or a distance modulus of (m-M)=5.63+-0.02. This
resolves the dispute between the main sequence fitting and the Hipparcos
distance moduli in favor of main sequence fitting.
