Online monitoring of rotor angle stability in wide area power systems is an important task to avoid out-of-step instability conditions. In recent years, the installation of phasor measurement units (PMUs) on the power grids has increased significantly and, therefore, a large amount of real-time data is available for online monitoring of system dynamics. This paper proposes a PMU-based application for online monitoring of rotor angle stability. A technique based on Lyapunov exponents is used to determine if a power swing leads to system instability. The relationship between rotor angle stability and maximal Lyapunov exponent (MLE) is established. A computational algorithm is developed for the calculation of MLE in an operational environment. The effectiveness of the monitoring scheme is illustrated with a three-machine system and a 200-bus system model.