This research is to apply the relatively new mathematical theory of chaos to earthquake catalogues in an attempt to extract the underlying attractor structure of the system. The question whether the methods of deterministic chaos are applicable to regional seismicity is highly relevant to models of earthquake occurrence and has received very little attention. A practical goal of this research is to see if the theory of chaos can be used to predict earthquakes and the work is thus a contribution to the National Earthquake Hazard Reduction Program.