For infrequent-event systems, transition state theory (TST) is a powerful approach for overcoming the time scale limitations of the molecular dynamics (MD) simulation method, provided one knows the locations of the potential-energy basins (states) and the TST dividing surfaces (or the saddle points) between them. Often, however, the states to which the system will evolve are not known in advance. We present a new, TST-based method for extending the MD time scale that does not require advanced knowledge of the states of the system or the transition states that separate them. The potential is augmented by a bias potential, designed to raise the energy in regions other than at the dividing surfaces. State to state evolution on the biased potential occurs in the proper sequence, but at an accelerated rate with a nonlinear time scale. Time is no longer an independent variable, but becomes a statistically estimated property that converges to the exact result at long times. The long-time dynamical behavior is exact if there are no TST-violating correlated dynamical events, and appears to be a good approximation even when this condition is not met. We show that for strongly coupled (i.e., solid state) systems, appropriate bias potentials can be constructed from properties of the Hessian matrix. This new "hyper-MD" method is demonstrated on two model potentials and for the diffusion of a Ni atom on a Ni(100) terrace for a duration of 20 mu s.