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In this paper, we study the problem of answering queries about private data that is spread across multiple different databases. For instance, a medical researcher may want to study a possible correlation between travel patterns and certain types of illnesses. The necessary information exists today - e.g., in airline reservation systems and hospital records - but it is maintained by two separate companies who are prevented by law from sharing this information with each other, or with a third party. This separation prevents the processing of such queries, even if the final answer, e.g., a correlation coefficient, would be safe to release. We present DJoin, a system that can process such distributed queries and can give strong differential privacy guarantees on the result. DJoin can support many SQL-style queries, including joins of databases maintained by different entities, as long as they can be expressed using DJoin's two novel primitives: BN-PSI-CA, a differentially private form of private set intersection cardinality, and DCR, a multi-party combination operator that can aggregate noised cardinalities without compounding the individual noise terms. Our experimental evaluation shows that DJoin can process realistic queries at practical timescales: simple queries on three databases with 15,000 rows each take between 1 and 7.5 hours.