Standard time series structure learning algorithms assume that the measurement timescale is approximately the same as the timescale of the underlying (causal) system. In many scientific contexts, however, this assumption is violated: the measurement timescale can be substantially slower than the system timescale (so intermediate time series datapoints will be missing). This assumption violation can lead to significant learning errors. In this paper, we provide a novel learning algorithm to extract system-timescale structure from measurement data that undersample the underlying system. We employ multiple algorithmic optimizations that exploit the problem structure in order to achieve computational tractability. The resulting algorithm is highly reliable at extracting system-timescale structure from undersampled data.