Pervasive internet and sensor technologies promise to revolutionize psychological science. However, the data collected using these technologies is often very personal - indeed the value of the data is often directly related to how personal it is. At the same time, driven by the replication crisis, there is a sustained push to publish data to open repositories. These movements are in fundamental conflict. In this paper, we propose a way to navigate this issue. We argue that there are significant advantages to be gained by ceding the ownership of data to the participants who generate it. Then we provide desiderata for a privacy-preserving platform. In particular, we suggest that researchers should use an interface to perform experiments and run analyses rather than observing the stimuli themselves. We argue that this method not only improves privacy but will also encourage greater compliance with good research practices than is possible with open repositories.