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There is a wide variety of condition monitoring techniques currently in use for the diagnosis and prediction of machinery faults, but little attention has been paid to the occurrence and detection of chaotic behaviour in time series vibration signals. This paper introduces some of the basic concepts of chaos theory, then details a method for quantifying a fractal dimension from a time series, the correlation dimension. Some of the practical difficulties encountered in measuring the correlation dimension from the correlation integral algorithm are also outlined. Finally, some experimental results from a rolling element bearing test rig are presented.