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The ground-state phase diagram of frustrated S=1 XXZ spin chains with thecompeting nearest- and next-nearest-neighbor antiferromagnetic couplings isstudied using the infinite-system density-matrix renormalization-group method.We find six different phases, namely, the Haldane, gapped chiral, gaplesschiral, double Haldane, N\'{e}el, and double N\'{e}el (uudd) phases. The gappedand gapless chiral phases are characterized by the spontaneous breaking ofparity, in which the long-range order parameter is a chirality, \kappa_l =S_l^xS_{l+1}^y-S_l^yS_{l+1}^x, whereas the spin correlation decays eitherexponentially or algebraically. These chiral ordered phases appear in a broadregion in the phase diagram for \Delta < 0.95, where \Delta is anexchange-anisotropy parameter. The critical properties of phase transitions arealso studied.Comment: 13 pages, 9 figures, to appear in J. Phys. Soc. Jp

Ground State Phase Diagram of Frustrated S = 1 XXZ chains: Chiral Ordered Phases