Chaos theory is being used as a tool to study a wide variety of phenomena. It is a philosophical and empirical approach that attempts to explain relationships previously thought to be totally random. Although some relationships are truly random, many data appear to be random but reveal repeatable patterns of behavior under further investigation. Chaos theory is concerned with chaotic systems that demonstrate: (1) constrained randomness; (2) self-referential systems (feedback mechanisms); and (3) fractals (dimensions that are a measure of the relative degree of complexity of an object). Another fundamental characteristic of chaotic systems is sensitivity to initial conditions. Many parallels exist between chaos theory and traditional research methodologies, as illustrated via a discussion of the concept of strange attractor (the phase space diagrams of chaotic systems), and much controversy surrounds applications of chaos theory. Because chaos theory is essentially systems oriented, it has many possible applications in education. The most immediate will come from study of individual brain function and how people learn. A new frontier in chaos theory is its application to organizational structures, which may give valuable insights into classroom structure and building and district organizations. Accuracy of communications, centralization versus decentralization, and control of disruptive behaviors in the classroom are a few examples of likely candidates for this type of research. Sixteen figures are included. (SLD)