Molecular dynamics simulation has been used to explore the evolution, kinetics. and dynamics of a liquid-glass transition in clusters and bulk matter. We demonstrate a dynamical indicator that characterizes the onset of the glass transition in clusters and is consistent with other indicators of glass transitions in bulk systems. This criterion, based on changes in chaotic behavior as measured by the largest Liapunov exponent, reveals aspects of the microscopic processes associated with the phase change from liquid to glass, and provides a connection between the thermodynamic and dynamical behavior of systems and their multidimensional potential surfaces.