A measurement of a part of the longitudinal acoustic mode of Teflon (polytetrafluoroethylene) is presented. The measurement was made utilizing the coherent inelastic scattering of low-energy neutrons. The sample consisted of extruded fibres in which the polymer axis was aligned along the fibre axis. The spectrometer used in the measurements provided a monochromatic neutron line incident on the sample obtained by Bragg scattering the reactor spectrum from a copper crystal. Time-of-flight techniques were used to energy analyze the scattered beam. The observed phonons agree well with a calculation of Boerio and Koenig.