An experiment has been performed to measure the total neutron cross section of the terphenyl mixture, known commercially as HB-40, for neutron energies in the range 0.002 to 1.6 eV. The cross sections were measured both for a fresh sample and for a sample that had a prolonged exposure to both neutron and gamma radiation. The microscopic cross sections due to scattering from the hydrogen nuclei in the material have been determined to an accuracy of better than 5% and have been compared to those of benzene (C6H6). The terphenyl cross sections are very similar to those of benzene.