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The clinical time-series setting poses a unique combination of challenges to data modeling and sharing. Due to the high dimensionality of clinical time series, adequate de-identification to preserve privacy while retaining data utility is difficult to achieve using common de-identification techniques. An innovative approach to this problem is synthetic data generation. From a technical perspective, a good generative model for time-series data should preserve temporal dynamics, in the sense that new sequences respect the original relationships between high-dimensional variables across time. From the privacy perspective, the model should prevent patient re-identification by limiting vulnerability to membership inference attacks. The NeurIPS 2020 Hide-and-Seek Privacy Challenge is a novel two-tracked competition to simultaneously accelerate progress in tackling both problems. In our head-to-head format, participants in the synthetic data generation track (i.e. "hiders") and the patient re-identification track (i.e. "seekers") are directly pitted against each other by way of a new, high-quality intensive care time-series dataset: the AmsterdamUMCdb dataset. Ultimately, we seek to advance generative techniques for dense and high-dimensional temporal data streams that are (1) clinically meaningful in terms of fidelity and predictivity, as well as (2) capable of minimizing membership privacy risks in terms of the concrete notion of patient re-identification.