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Time series motif discovery has been a fundamental task to identify meaningful repeated patterns in time series. Recently, time series chains were introduced as an expansion of time series motifs to identify the continuous evolving patterns in time series data. Informally, a time series chain (TSC) is a temporally ordered set of time series subsequences, in which every subsequence is similar to the one that precedes it, but the last and the first can be arbitrarily dissimilar. TSCs are shown to be able to reveal latent continuous evolving trends in the time series, and identify precursors of unusual events in complex systems. Despite its promising interpretability, unfortunately, we have observed that existing TSC definitions lack the ability to accurately cover the evolving part of a time series: the discovered chains can be easily cut by noise and can include non-evolving patterns, making them impractical in real-world applications. Inspired by a recent work that tracks how the nearest neighbor of a time series subsequence changes over time, we introduce a new TSC definition which is much more robust to noise in the data, in the sense that they can better locate the evolving patterns while excluding the non-evolving ones. We further propose two new quality metrics to rank the discovered chains. With extensive empirical evaluations, we demonstrate that the proposed TSC definition is significantly more robust to noise than the state of the art, and the top ranked chains discovered can reveal meaningful regularities in a variety of real world datasets.