Abstract We describe IXPE polarization observations of the pulsar wind nebula (PWN) MSH 15−5², the “Cosmic Hand.” We find X-ray polarization across the PWN, with B-field vectors generally aligned with filamentary X-ray structures. High-significance polarization is seen in arcs surrounding the pulsar and toward the end of the “jet,” with polarization degree PD > 70%, thus approaching the maximum allowed synchrotron value. In contrast, the base of the jet has lower polarization, indicating a complex magnetic field at significant angle to the jet axis. We also detect significant polarization from PSR B1509−58 itself. Although only the central pulse phase bin of the pulse has high individual significance, flanking bins provide lower-significance detections and, in conjunction with the X-ray image and radio polarization, can be used to constrain rotating vector model solutions for the pulsar geometry.