From Diablo Wiki
Project Hydra was the codename for Diablo III during development at Blizzard North from 2000-2005, and then at Blizzard Irvine from 2006-2008, until Diablo III was revealed in June 2008 at the World Wide Invitational in Paris, France.
As the Sorceress' Hydra skill summoned a three-headed flaming dragon in Diablo II, this wasn't one of the most mysterious project code nicknames ever invented.
Many of the doors in the Diablo III teams' section of Blizzard's offices in Irvine still bore "Project Hydra" plaques when fansites were allowed to visit in 2009.
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