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We have completed a kinematic study of the fast-moving, oxygen-rich filaments identified in the Puppis A supernova remnant by Winkler and Kirshner (1985, ApJ, 299, 981). These filaments, which have high oxygen and neon abundances and almost no hydrogen, are probably shards of supernova ejecta that have remained almost undiluted and undecelerated by interaction with the ISM -- similar to the fast-moving knots in Cas A.\ \ Proper motions of several knots, measured over an 8-year baseline by Winkler et al. (1988, IAU Colloq 101, 65), are typically 0.1 to 0.2 arcsec~yr$^{-1}$\ and are consistent with undecelerated expansion from a supernova event 3700 years ago. New spectra of 11 of these filaments, obtained from the CTIO 4-m, give radial velocities from $-1600$ to $+1000$ km~s$^{-1}$. A model in which all the filaments lie on a uniformly expanding spherical shell is consistent with the data and indicates an expansion velocity of 1870 km~s$^{-1}$. Combination of the proper motions and radial velocities yields a kinematic distance to Puppis A of 1.9 kpc, a value consistent with previous values from based on less direct methods. Puppis A now becomes one of the mere handful of remnants with a kinematically determined distance.
