We present results from X-ray and radio observations of the recently discovered young Vela-like pulsar PSR J2021+3651, which is coincident with the EGRET gamma-ray source GeV 2020+3658. A 19.0-ks Chandra ACIS-S observation has revealed a ~20 x 10 pulsar wind nebula that is reminiscent of the equatorial tori seen around some young pulsars, along with thermal emission from an embedded point source (kT = 0.15 +/- 0.02 keV). We name the nebula G75.2+0.1. Its spectrum is well fit by an absorbed power-law model with photon index 1.7 +/- 0.3, hydrogen column density nH = 7.8 +/- 1.7 x 10^21 cm^-2, and an unabsorbed 0.3-10.0 keV flux of 1.9 +/- 0.3 x 10^-12 erg cm^-2 s^-1. We have spatially fit G75.2+0.1 with a model that assumes a toroidal morphology, and from this we infer that the torus is highly inclined 83 deg +/- 1 deg to the line of sight. A 20.8-ks Chandra observation in continuous-clocking mode reveals a possible pulse detection, with a pulsed fraction of ~37% and an H-test probability of occuring by chance of 1.2 x 10^-4. Timing observations with the Arecibo radio telescope spanning two years show that PSR J2021+3651 glitched sometime between MJDs 52616 and 52645 with parameters delta(v)/v = (2.587 +/- 0.002) x 10^-6 and delta(dot(v))/v = (6.2 +/- 0.3) x 10^-3, similar to those of the largest glitches observed in the Vela pulsar. PSR J2021+3651 is heavily scattered (T_sc = 17.7 ms +/- 0.9 ms at 1 GHz) and exhibits a significant amount of timing noise.
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