The South Pole Telescope (SPT) has probed an expanded angular range of the CMB temperature power spectrum. Their recent analysis of the latest cosmological data prefers nonzero neutrino masses, mnu = 0.32+-0.11 eV. This result, if confirmed by the upcoming Planck data, has deep implications on the discovery of the nature of neutrinos. In particular, the values of the effective neutrino mass involved in neutrinoless double beta decay (bb0nu) are severely constrained for both the direct and inverse hierarchy, making a discovery much more likely. In this paper, we focus in xenon-based bb0nu experiments, on the double grounds of their good performance and the suitability of the technology to large-mass scaling. We show that the current generation, with effective masses in the range of 100 kg and conceivable exposures in the range of 500 kg year, could already have a sizable opportunity to observe bb0nu events, and their combined discovery potential is quite large. The next generation, with an exposure in the range of 10 ton year, would have a much more enhanced sensitivity, in particular due to the very low specific background that all the xenon technologies (liquid xenon, high-pressure xenon and xenon dissolved in liquid scintillator) can achieve. In addition, a high-pressure xenon gas TPC also features superb energy resolution. We show that such detector can fully explore the range of allowed effective Majorana masses, thus making a discovery very likely.