The shape of the thorium absorption cross section near thermal energies was investigated. This shape is dominated by one or more negative energy resonances whose parameters are not directly known but must be inferred from higher energy data. Since the integral quantity most conveniently describing the thermal cross-section shape is the Westcott g-factor, effort was directed toward establishing this quantity to high precision. Three nearly independent g-factor estimates were obtained from measurements on a variety of foils in three different neutron spectra provided by polyethylene-moderated neutrons from a 252Cf source and from irradiations in the National Bureau of Standards “Standard Thermal Neutron Density.” The weighted average of the three measurements was 0.990 ± 0.009. This is in good agreement with two recent evaluations and supports the adequacy of the current cross-section descriptions.