We have used Brillouin light scattering (BLS) to measure the glass transition temperature of thin, freely-standing poly(styrene) (PS) films. The freely-standing films were prepared by spincoating solutions of PS in toluene onto glass substrates, annealing the supported films in vacuum, and then using a water surface transfer technique to place the films across a 3 mm diameter orifice. Ellipsometry measurements of similar floated films transferred to Si(001) wafers allow the determination of the film thicknesses. Atomic force microscopy measurements revealed that the films have an rms roughness of less than 10 A˚. With the freely-standing films placed in an optical furnace, we performed BLS measurements of the films using a high-contrast, multipassed, tandem Fabry-Perot interferometer. We obtained a reliable, reproducible measure of the glass transition temperature, Tg, from the large changes in the frequencies of the thermally-excited, viscoelastic, film-guided waves within the PS films as the films were heated above Tg. BLS results for bulk PS and a 1800 A˚ thick, freely-standing PS film are presented. We find the same glass transition temperature for the 1800 A˚ thick film as the bulk PS sample. This Tg value is the same as that obtained using differential scanning calorimetry (DSC).