Summary: The probabilistic element of quantum theory can be combined with the unitary time evolution of Schrödinger's equation in a natural and consistent way using the idea of a quantum trajectory, the quantum analog of the trajectory traced out in phase space as a function of time by a point representing the state of a closed classical system. A family of quantum trajectories can be defined using bases for the quantum Hilbert space at different times chosen so that an appropriate noninterference condition, related to the Gell-Mann and Hartle notion of medium decoherence, is satisfied. The result is a generalization of the consistent histories approach to quantum mechanics.