We have analyzed HST Wide Field Camera CCD images of Pluto, Charon, and a background star to observe Pluto's barycentric motion and to determine the individual masses and bulk densities of Pluto and Charon. The most fundamental new result was an accurate solution for a previously undetermined parameter, the Charon/Pluto mass ratio q; the new solution is q = 0.0837 +/- 0.0147. Significant accuracy improvements by almost a factor of two were obtained for Charon's orbital semimajor axis, a = 19,405 +/- 86 km and the Pluto system mass of 1.401 +/- 0.019 x 10 exp 8 inverse solar masses. The Pluto and Charon masses were (13.10 +/- 0.24) x 10 exp 24 g and (1.10 +/- 0.18) x 10 exp 24 g, respectively. Computed densities depend strongly on the assumed radius values. The density of Pluto is 2.13 +/- 0.04 g/cu cm and that of Charon is 1.30 +/- 0.23 g/cu cm.