Chatter in machining results in poor workpiece surface quality and short tool life. An accurate and reliable chatter detection method is needed before its complete development. This paper applies a novel p-leader multifractal formalism for chatter detection in milling processes. This novel formalism can discover internal singularities rising on unstable signals due to chatter without prior knowledge of the natural frequencies of the machining system. The p-leader multifractal features are selected by using a multivariate filter method for feature selection, and verified by both numerical simulations and experimental studies with detailed parameter selection discussions when applying this formalism. The proposed method is assessed in terms of their dynamic monitoring abilities and classification accuracies under wide cutting conditions. The results show that the multifractal features can successfully detect chatter with high accuracies and short computation time. For further verification, the proposed method is compared with two commonly-used methods, which indicates that the proposed method gives better classification accuracies, especially when identifying unstable tests.