We present observations with the Chandra X-ray Observatory of the pulsar wind nebula ( PWN ) powered by the energetic young pulsar B1509–58 . These data confirm the complicated morphology of the system indicated by previous observations , and in addition reveal several new components to the nebula . The overall PWN shows a clear symmetry axis oriented at a position angle 150 ^ { \circ } \pm 5 ^ { \circ } ( north through east ) , which we argue corresponds to the pulsar spin axis . We show that a previously identified radio feature matches well with the overall extent of the X-ray PWN , and propose the former as the long-sought radio nebula powered by the pulsar . We further identify a bright collimated feature , at least 4 ^ { \prime } long , lying along the nebula ’ s main symmetry axis ; we interpret this feature as a physical outflow from the pulsar , and infer a velocity for this jet > 0.2 c . The lack of any observed counter-jet implies that the pulsar spin axis is inclined at \sim 30 ^ { \circ } to the line-of-sight , contrary to previous estimates made from lower-resolution data . We also identify a variety of compact features close to the pulsar . A pair of semi-circular X-ray arcs lie 17 ^ { \prime \prime } and 30 ^ { \prime \prime } to the north of the pulsar ; the latter arc shows a highly-polarized radio counterpart . We show that these features can be interpreted as ion-compression wisps in a particle-dominated equatorial flow , and use their properties to infer a ratio of electromagnetic to particle energy in pairs at the wind shock \sigma \sim 0.005 , similar to that seen in the Crab Nebula . We further identify several compact knots seen very close to the pulsar ; we use these to infer \sigma < 0.003 at a separation from the pulsar of 0.1 pc .