Using neutron diffraction, 170Yb Mössbauer and muon spin relaxation spectroscopies, we have examined the pyrochlore Yb2Ti2O7, where the Yb3+S' = 1/2 ground state has planar anisotropy. Below approximately 0.24 K, the temperature of the known specific-heat lambda transition, there is no long range magnetic order. We show that the transition corresponds to a first-order change in the fluctuation rate of the Yb3+ spins. Above the transition temperature, the rate, in the GHz range, follows a thermal excitation law, whereas below, the rate, in the MHz range, is temperature independent, indicative of a quantum fluctuation regime.