In organic inclusion compounds the strong and restrictive polymer-polymer intermolecular interactions of the bulk polymer crystal are replaced with the less limiting geometrical constraints of the channel walls. This facilitates the study of isolated polymer molecules in the solid state. In this report we present the results of a deuterium NMR analysis of the motions of fully extended polyethylene chains confined to the 5 Angstrom diameter channels of the inclusion compound formed with perhydrotriphenylene. Line shape analysis and relaxation data demonstrate that the most important motion is that of the high-frequency libration of the carbon-carbon bonds about the traits conformational arrangement. This bond libration effects a low-energy twisting motion that provides a complete reorientation of the C-D bonds about the long axis of the molecule on the nanosecond time scale. A broad distribution of frequencies is associated with this motion.