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We present an absolute parallax and relative proper motion for thefundamental distance scale calibrator, RR Lyr. We obtain these with astrometricdata from FGS 3, a white-light interferometer on HST. We find $\pi_{abs} = 3.82\pm 0.2$ mas. Spectral classifications and VRIJHKT$_2$M and DDO51 photometry ofthe astrometric reference frame surrounding RR Lyr indicate that fieldextinction is low along this line of sight. We estimate <A_V>=0.07\pm0.03 forthese reference stars. The extinction suffered by RR Lyr becomes one of thedominant contributors to the uncertainty in its absolute magnitude. Adoptingthe average field absorption, <A_V>=0.07 \pm 0.03, we obtain M_V^{RR} = 0.61^{-0.11}_{+0.10}. This provides a distance modulus for the LMC, m-M = 18.38 -18.53^{-0.11}_{+0.10} with the average extinction-corrected magnitude of RR Lyrvariables in the LMC, <V(RR)>, remaining a significant uncertainty. We comparethis result to more than 80 other determinations of the distance modulus of theLMC.Comment: Several typos corrected. To appear in The Astronomical Journal,  January 200

Astrometry with the [ITAL]Hubble Space Telescope[/ITAL]: A Parallax of the Fundamental Distance Calibrator RR Lyrae