At normal conditions crystalline polyethylene (PE) has an orthorhombic structure, whereas at high pressure (above 3200 bar) a phase with a hexagonal structure occurs. We investigate the effect of high pressure (up to about 5000 bar) on the chain motion in PE in the orthorhombic structure and in the vicinity of the transformation to the hexagonal phase. From proton and deuteron NMR spectra and spin-lattice relaxation rates we conclude that, apart from high-frequency mobility at defects, the rigid orthorhombic structure only allows small-angle reorientation of the CH2 groups on a time scale of the order of 10(-7) s. The application of high pressure results in a considerable reduction of the amplitude of this motion. The degree of crystallinity is found to increase spectacularly by solidification from the hexagonal phase.