A Chandra study of a pulsar wind nebula around the young energetic pulsar PSR B1509−58 is presented. A high-resolution X-ray image with a total exposure time of 190 ks reveals a ringlike feature 10'' apart from the pulsar. This feature is analogous to the inner ring seen in the Crab nebula, and thus may correspond to wind termination shock. The shock radius enables us to constrain the wind magnetization, σ ≥ 0.01, which is one order of magnitude larger than that of the Crab nebula. In the vicinity of the pulsar, the south jet appears to be as broad as the diameter of the inner ring at its beginning, in contrast to the narrow jet of the Crab. This morphology of the broad jet is consistent with a recently proposed theoretical model in which magnetic hoop stress diverts and squeezes the postshock equatorial flow toward the poloidal direction, generating a jet.