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A self-consistent model for binary evolution devised by Gingold \& Monaghan(1980) is used to show that two distinctly different types of behaviour arepossible for close eccentric binaries. The model is based on a linear adiabaticnormal mode analysis of the problem, which allows detailed examination of thetransfer of energy from the orbit to the tides. We show that for most binaries,energy is exchanged quasi-periodically, with the system regulating itself sothat the maximum tidal energy always remains small, and no circularizationtakes place. In contrast, for a range of eccentricities and periastronseparations, {\it chaotic} behaviour prevails, with the eccentricity followinga random walk and with the energy transferred to the tides during a singleperiastron passage being up to an order of magnitude larger than thattransferred during the initial periastron passage.  These results have important consequences for the study of tidal capturebinaries. The standard model (see, for example, McMillan, McDermott \& Taam1987) assumes that the energy transferred to the tides during a periastronencounter is independent of the oscillatory state of the stars, and that theamount of tidal energy present at any time can be calculated using a formulawhich (accurately) gives the amount deposited after the first encounter (Press\& Teukolsky 1977). The calculations presented here show that a self-consistenttreatment is necessary in order to study the dynamical evolution of tidalcapture binaries. We conclude that the tidal capture process would not bepossible were it not for the existence of chaotic behaviour.

The Role of Chaos in the Circularization of Tidal Capture Binaries. I. The Chaos Boundary