Quantum mechanics with a nonzero quantum correlation time

We propose an extension of quantum mechanics based on the idea that the underlying "quantum noise" has a nonzero, albeit very small, correlation time tau(c). The standard (nonrelativistic) Schrodinger equation is recovered to zeroth order in tau(c), and the first correction to energy levels is computed. Some consequences are discussed, in particular, the violation of Heisenberg's uncertainty principle and the restoration of locality at short times.