A Chandra study of pulsar wind nebula around the young energetic pulsar PSR B1509 - 58 is presented . The high resolution X-ray image with total exposure time of 190 ks reveals a ring like feature 10 ” apart from the pulsar . This feature is analogous to the inner ring seen in the Crab nebula and thus may correspond to a wind termination shock . The shock radius enables us to constrain the wind magnetization , \sigma \geq 0.01 . The obtained \sigma is one order of magnitude larger than that of the Crab nebula . In the pulsar vicinity , the southern jet appears to extend beyond the wind termination shock , in contrast to the narrow jet of the Crab . The revealed morphology of the broad jet is coincident with the recently proposed theoretical model in which a magnetic hoop stress diverts and squeezes the post-shock equatorial flow towards the poloidal direction generating a jet .