We propose a quantum analogue of the notion of empirical measure in the context of the quantum mechanics of systems of identical particles. We write a dynamical equation for this new object, and prove that the Hartree equation coincides with this dynamics for a special class of quantum empirical measures corresponding to the chaotic limit. This is on a par with the theory of Klimontovich solutions of the Vlasov equation. As an application, we give an $O(1/\sqrt{N})$ convergence rate for the mean-field limit in quantum mechanics uniformly in the Planck constant, for smooth interaction potentials.