In this paper, a novel approach to predict turning points for chaotic financial time series is proposed based on chaotic theory and machine learning. The nonlinear mapping between different data points in primitive time series is derived and proven. Our definition of turning points produces an event characterization function, which can transform the profile of time series to a measure. The RBF neural network is further used as a nonlinear modeler. We discuss the threshold selection and give a procedure for threshold estimation using out-of-sample validation. The proposed approach is applied to the prediction problem of two real-world financial time series. The experimental results validate the effectiveness of our new approach.