An oracle is a service that provides data to smart contracts or other systems. Oracles obtain their data from trusted websites. But even those that relay data correctly cannot safely access users' web-session data, because they can't enforce privacy. DECO is a privacy-preserving oracle protocol. Using cryptographic techniques, it lets users prove facts about their web (TLS) sessions to oracles while hiding privacy-sensitive data. DECO can make private and public web data accessible to a rich spectrum of applications, for blockchains and traditional (non-blockchain) systems.