Digital storage of personal music collections and cloud-based music services (e.g. Pandora, Spotify) have fundamentally changed how music is consumed. In particular, automatically generated playlists have become an important mode of accessing large music collections. The key goal of automated playlist generation is to provide the user with a coherent listening experience. In this paper, we present Latent Markov Embedding (LME), a machine learning algorithm for generating such playlists. In analogy to matrix factorization methods for collaborative filtering, the algorithm does not require songs to be described by features a priori, but it learns a representation from example playlists. We formulate this problem as a regularized maximum-likelihood embedding of Markov chains in Euclidian space, and show how the resulting optimization problem can be solved efficiently. An empirical evaluation shows that the LME is substantially more accurate than adaptations of smoothed n-gram models commonly used in natural language processing.