Cyberbullying is a major problem affecting more than half of all American teens. Prior work has largely focused on detecting cyberbullying after the fact. In this paper, we investigate the prediction of cyberbullying incidents in Instagram, a popular media-based social network. The novelty of this work is building a predictor that can anticipate the occurrence of cyberbullying incidents before they happen. The Instagram media-based social network is well-suited to such prediction since there is an initial posting of an image typically with an associated text caption, followed later by the text comments that form the basis of a specific cyberbullying incident. We extract several important features from the initial posting data for automated cyberbullying prediction, including profanity and linguistic content of the text caption, image content, as well as social graph parameters and temporal content behavior. Evaluations using a real-world Instagram dataset demonstrate that our method achieves high performance in predicting the occurrence of cyberbullying incidents.