Action segmentation, inferring temporal positions of human actions in an untrimmed video, is an important prerequisite for various video understanding tasks. Recently, unsupervised action segmentation (UAS) has emerged as a more challenging task due to the unavailability of frame-level annotations. Existing clustering- or prediction-based UAS approaches suffer from either over-segmentation or overfitting, leading to unsatisfactory results. To address those problems,we propose Predictive And Contrastive Embedding (PACE), a unified UAS framework leveraging both predictability and similarity information for more accurate action segmentation. On the basis of an auto-regressive transformer encoder, predictive embeddings are learned by exploiting the predictability of video context, while contrastive embeddings are generated by leveraging the similarity of adjacent short video clips. Extensive experiments on three challenging benchmarks demonstrate the superiority of our method, with up to 26.9% improvements in F1-score over the state of the art.