  Bose-Einstein correlations of identical hadrons reveal information about
hadron creation from the strongly interacting matter formed in
ultrarelativistic heavy ion collisions. The measurement of three-particle
correlations may in particular shed light on hadron creation mechanisms beyond
thermal/chaotic emission. In this paper we show the status of PHENIX
measurements of three pion correlations as a function of momentum differences
within the triplets. We analyze the shape of the correlation functions through
the assumption of L\'evy sources and a proper treatment of the Coulomb
interaction within the triplets. We measure the three-particle correlation
strength ($\lambda_3$), which, together with the two-particle correlation
strength $\lambda_2$, encodes information about hadron creation mechanisms.
From a consistent analysis of two- and three-particle correlation strength we
establish a new experimental measure of thermalization and coherence in the
source.
