Sulphur trioxide (SO_3_) is a trace species in the atmospheres of the Earth and Venus, as well as being an industrial product and an environmental pollutant. A variational line list for ^32^S_16_O_3_, named UYT2, is presented containing 21 billion vibration-rotation transitions. UYT2 can be used to model infrared spectra of SO3 at wavelengths longwards of 2um (nu<5000cm^-1^) for temperatures up to 800K. Infrared absorption cross-sections recorded at 300 and 500 C are used to validate the UYT2 line list. The intensities in UYT2 are scaled to match the measured cross-sections. The line list is made available in electronic form as supplementary data to this article and at www.exomol.com.