By applying a nuclear magnetic resonance (n.m.r.) multiple pulse sequence to a powder of randomly aligned crystallites, the principal values of the chemical shift tensor may be measured. However information about alignment of the chemical shift tensor with respect to the crystal axes is lost. To obtain orientation information in polytetrafluoroethylene (PTFE), we have prepared a bundle of drawn PTFE fibres and observed the 19F line-narrowed n.m.r. spectra for various fibre orientations relative to the direction of the static magnetic field. The data at 77 K indicate that the most screened component of the chemical shift tensor lies along the C-F bond and that the least screened component is aligned at approximately 20° to the molecular chain axis. At 298K the spectrum of a PTFE powder indicates an axially symmetrical tensor whose principal values are consistent with a 20° inclination of the least screened component relative to the chain axis.