We describe recent Chandra ACIS observations of the Vela-like pulsar PSR J2021+3651 and its pulsar wind nebula (PWN). This `Dragonfly Nebula displays an axisymmetric morphology, with bright inner jets, a double-ridged inner nebula, and a ~30 polar jet. The PWN is embedded in faint diffuse emission: a bow shock-like structure with standoff ~1 brackets the pulsar to the east and emission trails off westward for 3-4. Thermal (kT=0.16 +/-0.02 keV) and power law emission are detected from the pulsar. The nebular X-rays show spectral steepening from Gamma=1.5 in the equatorial torus to Gamma=1.9 in the outer nebula, suggesting synchrotron burn-off. A fit to the `Dragonfly structure suggests a large (86 +/-1 degree) inclination with a double equatorial torus. Vela is currently the only other PWN showing such double structure. The >12 kpc distance implied by the pulsar dispersion measure is not supported by the X-ray data; spectral, scale and efficiency arguments suggest a more modest 3-4 kpc.
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