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 \sim 20 ^ { \prime \prime } \times 10 ^ { \prime \prime } 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 _ { \infty } = 0.15 \pm 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 \Gamma = 1.7 ^ { +0.3 } _ { -0.2 } , hydrogen column density n _ { H } = ( 7.8 ^ { +1.7 } _ { -1.4 } ) \times 10 ^ { 21 } cm ^ { -2 } , and an unabsorbed 0.3 - 10.0 keV flux of ( 1.9 ^ { +0.1 } _ { -0.3 } ) \times 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 ^ { \circ } \pm 1 ^ { \circ } ) 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 \sim 37 % and an H-test probability of occuring by chance of 1.2 \times 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 \nu } / { \nu } = ( 2.587 \pm 0.002 ) \times 10 ^ { -6 } and { \Delta \dot { \nu } } / { \dot { \nu } } = ( 6.2 \pm 0.3 ) \times 10 ^ { -3 } , similar to those of the largest glitches observed in the Vela pulsar . PSR J2021+3651 is heavily scattered ( { \tau } _ { sc } = 17.7 \pm 0.9 ms at 1 GHz ) and exhibits a significant amount of timing noise .