Compton scattering of the cosmic microwave background (CMB) from hot ionized gas produces a range of effects, and the leading order effects are the kinetic and thermal Sunyaev Zel'dovich (kSZ and tSZ) effects. In the near future, CMB surveys will provide the precision to probe beyond the leading order effects. In this Letter, we study the cosmological information content of the next order term which combines the tSZ and kSZ effects, hereafter called the thermal-kinetic Sunyaev Zel'dovich (tkSZ) effect. As the tkSZ effect has the same velocity dependence as the kSZ effect, it will also have many of the useful properties of the kSZ effect. However, it also has its own, unique spectral dependence, which allows it to be isolated from all other CMB signals. We show that with currently envisioned CMB missions the tkSZ effect can be detected and can be used to reconstruct large scale velocity fields, with no appreciable bias from either the kSZ effect or other extragalactic foregrounds. Furthermore, since the tkSZ effect arises from the well-studied pressure of ionized gas, rather than the gas number density as in the kSZ effect, the degeneracy due to uncertain gas physics will be significantly reduced. Finally, for a very low-noise experiment the tkSZ effect will be measurable at higher precision than the kSZ effect.