We report a precise measurement of the parity-violating (PV) asymmetry APV in the elastic scattering of longitudinally polarized electrons from Ca-48. We measure A(PV) = 2668 +/- 106(stat) +/- 40(syst) parts per billion, leading to an extraction of the neutral weak form factor F-W(q = 0.8733 fm(-1)) = 0.1304 +/- 0.0052(stat) +/- 0.0020(syst) and the charge minus the weak form factor F-ch -F-W = 0.0277 +/- 0.0055. The resulting neutron skin thickness R-n - R-p = 0.121 +/- 0.026(exp) +/- 0.024(model) fm is relatively thin yet consistent with many model calculations. The combined CREX and PREX results will have implications for future energy density functional calculations and on the density dependence of the symmetry energy of nuclear matter.