Kac's (stochastic) model describes the time-evolution of the velocities of homogeneously situated particles that, upon random binary collision, redistribute their kinetic energies in a way that conserves the total energy of the many particle system. In this joint work with Jani Lukkarinen, we study the time-evolution of the (joint) cumulant hierarchy of the system and its time-evolution. We prove that the higher order "correlations" between the kinetic energies of the particles become negligible quickly, exhibiting what could be described as the generation of chaos.