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Knowledge of future channel conditions can increase the performance of many types of wireless systems. This is especially true for radio channels with multiple transmit and receive antennas, i.e. multiple-input multiple-output (MIMO) systems. This paper derives a performance bound for MIMO channel prediction. It is assumed that prediction is based upon estimating a model for the channel and then extrapolating that model to predict future values of the channel. A vector formulation of the Cramer-Rao bound for functions of parameters is then used to find a lower bound on the prediction error. Numerical evaluation of this bound shows that substantially longer prediction lengths are possible for MIMO channels than for single antenna channels. An intuitive interpretation of this result is that more of the channel structure is revealed when using multiple antennas at both ends.