In this paper we present the first results of a privacy-preserving system designed to enable safe sharing and replication of statistical analysis computed from sensitive datasets. Our system is composed of three elements, all of them made available to the scientific community thanks to an effort lead by the Institute for Quantitative Social Science at Harvard University. First, we use differential privacy, a privacy-preserving technique that avoids re-identification while preserving the statistical properties of the sensitive dataset. Second, we use the Dataverse open source software to share the resulting statistics consistently with FAIR principles, including automatic citation, persistent identifiers and data provenance. Third, we apply a simplified Datatags implementation to enable access to any sensitive dataset required for replication.