Time series motifs were introduced in 2002, and have since become a fundamental tool for time series analytics, finding diverse uses in dozens of domains. In this work we introduce Time Series Chains, which are related to, but distinct from, time series motifs. Informally, time series chains are a temporally ordered set of subsequence patterns, such that each pattern is similar to the pattern that preceded it, but the first and last patterns can be arbitrarily dissimilar. In the discrete space, this is similar to extracting the text chain “data, date, cate, cade, code” from text stream. The first and last words have nothing in common, yet they are connected by a chain of words with a small mutual difference. Time series chains can capture the evolution of systems, and help predict the future. As such, they potentially have implications for prognostics. In this work, we introduce two robust definitions of time series chains, and scalable algorithms that allow us to discover them in massive complex datasets.