We have examined Chandra observations of the recently discovered X-ray thread G0.13-0.11 in the Galactic center Radio Arc region. Part of the Chandra data was studied by Yusef-Zadeh, Law, & Wardle, who reported the detection of 6.4 keV line emission in this region. We find, however, that this line emission is not associated with G0.13-0.11. The X-ray spectrum of G0.13-0.11 is well-characterized by a simple power law with an energy slope of 1.8 (90% confidence uncertainties). Similarly, the X-ray spectrum of the pointlike source embedded in G0.13-0.11 has a power-law energy slope of 0.9. The 2-10 keV band luminosities of these two components are ~3.2 × 1033 ergs s-1 (G0.13-0.11) and ~7.5 × 1032 ergs s-1 (point source) at the Galactic center distance of 8 kpc. The morphological, spectral, and luminosity properties strongly indicate that G0.13-0.11 represents the leading edge of a pulsar wind nebula, produced by a pulsar (point source) moving in a strong magnetic field environment. The main body of this pulsar wind nebula is likely traced by a bow-shaped radio feature, which is apparently bordered by G0.13-0.11 and is possibly associated with the prominent nonthermal radio filaments of the Radio Arc. We speculate that young pulsars may be responsible for various unique nonthermal filamentary radio and X-ray features observed in the Galactic center region.