Advances within the new science of Chaos have enabled scientists in several disparate disciplines to deepen their understanding of complex systems and to quantify certain phenomena called state transitions. These transitions occur where the nature of the system changes markedly, for example, when a fluid passes from smooth to turbulent flow. Nonlinear systems (those that are modelled best by Chaos) are described in this paper and compared with psychoanalytic models of the mind. Some psychoanalytic phenomena are examined in the light of the principles of Chaos. The author asserts that there are sufficient correspondences between operative models in those disciplines that have benefited from the use of principles of Chaos and psychoanalytic models of the mind to warrant theoretical and experimental efforts in the use of those principles. Such efforts could enhance our understanding of the mind and may suggest a new methodology for psychoanalytic research.