A hatchery was a facility where a species's young were hatched from eggs.
Several Xindi-Insectoid ships had hatcheries that were incubation facility for the crew's eggs. (ENT: "Hatchery")
The Dominion bred the Jem'Hadar in hatcheries. (DS9: "Penumbra")
Jem'Hadar hatcheries presumably included Birthing chambers.
In David Weddle and Jeffrey Lang's Deep Space Nine and Star Trek: Section 31 novel "Abyss", Ethan Locken at Memory Beta, the wiki for licensed Star Trek works, a rogue Section 31 member, uses an abandoned hatchery to breed Jem'Hadar soldiers loyal to him.
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