Global polarization of Xi and Omega hyperons has been measured for the first time in Au + Au collisions at root S-NN= 200 GeV. The measurements of the Xi(-) and (Xi) over bar (+) hyperon polarization have been performed by two independent methods, via analysis of the angular distribution of the daughter particles in the parity violating weak decay Xi -> Lambda + pi, as well as by measuring the polarization of the daughter A hyperon, polarized via polarization transfer from its parent. The polarization, obtained by combining the results from the two methods and averaged over Xi(-) and (Xi) over bar (+), is measured to be < P-Xi > = 0.47 +/- 0.10(stat) +/- 0.23(syst)% for the collision centrality 20%-80%. The < P-Xi > is found to be slightly larger than the inclusive Lambda polarization and in reasonable agreement with a multiphase transport model. The < P-Xi > is found to follow the centrality dependence of the vorticity predicted in the model, increasing toward more peripheral collisions. The global polarization of Omega, < P-Omega > = 1.11 +/- 0.87(stat) +/- 1.97(syst)% was obtained by measuring the polarization of daughter Lambda in the decay Omega -> Lambda + K, assuming the polarization transfer factor C-Omega Lambda = 1.