Since their introduction over a decade ago, time series motifs have 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 are arbitrarily dissimilar. In the discrete space, this is similar to extracting the text chain "hit, hot, dot, dog" from a paragraph. 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 a robust definition of time series chains, and a scalable algorithm that allows us to discover them in massive datasets.