Thermoacoustic tomography (TCT) is a hybrid imaging technique that has been proposed as an alternative to xray mammography. Ideally, electromagnetic (EM) energy is deposited into the breast tissue uniformly in space, but impulsively in time. This heats the tissue causing thermal expansion. Cancerous masses absorb more energy than healthy tissue, creating a pressure wave, which is detected by standard ultrasound transducers placed on the surface of a hemisphere surrounding the breast. Assuming constant sound speed and zero attenuation, the data represent integrals of the tissue's EM absorptivity over spheres centered about the receivers (ultrasound transducers). The inversion problem for TCT is therefore to recover the EM absorptivity from integrals over spheres centered on a hemisphere. We present an inversion formula for the complete data case, where integrals are measured for centers on the entire sphere. We discuss differences between ideal and clinically measurable TCT data and options for accurately reconstructing the latter.