We report the first measurement of the parity-violating asymmetry A(PV) in the elastic scattering of polarized electrons from Pb-208. APV is sensitive to the radius of the neutron distribution (R-n). The result A(PV) = 0.656 +/- 0.060(stat) +/- 0.014(syst) ppm corresponds to a difference between the radii of the neutron and proton distributions R-n - R-p = 0.33(-0.18)(+0.16) fm and provides the first electroweak observation of the neutron skin which is expected in a heavy, neutron-rich nucleus.