We present high-resolution Chandra X-ray observations of PSR B0833[45, the 89 ms pulsar associated with the Vela supernova remnant. We have acquired two observations separated by 1 month to search for changes in the pulsar and its environment following an extreme glitch in its rotation frequency. We Ðnd a well-resolved nebula with a toroidal morphology remarkably similar to that observed in the Crab Nebula, along with an axial Crab-like jet. Between the two observations, taken D3 ] 105 s and D3 ] 106 s after the glitch, the Ñux from the pulsar is found to be steady to within 0.75% ; the 3 p limit on the fractional increase in the pulsarÏs X-ray Ñux is of the inferred glitch energy. We use [10~5 this limit to constrain parameters of glitch models and neutron star structure. We do Ðnd a signiÐcant increase in the Ñux of the nebulaÏs outer arc ; if associated with the glitch, the inferred propagation velocity is similar to that seen in the brightening of the Crab Nebula wisps. We propose an explana-Z0.7c, tion for the X-ray structure of the Vela synchrotron nebula based on a model originally developed for the Crab Nebula. In this model, the bright X-ray arcs are the shocked termination of a relativistic equatorial pulsar wind that is contained within the surrounding kidney-bean shaped synchrotron nebula comprising the postshock, but still relativistic, Ñow. In a departure from the Crab model, the magnetization parameter p of the Vela pulsar wind is allowed to be of order unity ; this is consistent with the simplest MHD transport of magnetic Ðeld from the pulsar to the nebula, where B ¹ 4 ] 10~4 G. The inclination angle of the axis of the equatorial torus with respect to the line of sight is identical to that of the rotation axis of the pulsar as previously measured from the polarization of the radio pulse. The projection of the rotation axis on the sky may also be close to the direction of proper motion of the pulsar if previous radio measurements were confused by orthogonal-mode polarized components. We review e †ects that may enhance the probability of alignment between the spin axis and space velocity of a pulsar, and speculate that short-period, slowly moving pulsars are just the ones best-suited to producing synchrotron nebulae with such aligned structures. Previous interpretations of the compact Vela nebula as a bow-shock in a very weakly magnetized wind su †ered from data of inadequate spatial resolution and less plausible physical assumptions.