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The quest starts after you talk to Chrissy's mother in the Vault 15 squat. After you exit dialogue, follow the rocky path that leads to the green exit grid and talk to Dalia.
If your speech skill is too low, you'll have to kill Dalia to get by her, otherwise, you'll convince her to leave. Either way, when Dalia is out of the way, enter the next area.
Here you will encounter two raiders. One in front of the shack and another inside. High speech will enable you to free Chrissy without firing a bullet; alternatively, you can gun the raiders down. Be warned though, as the door to the room holding Chrissy is trapped, while one of the raiders, Phil, holds a key to it. After you free Chrissy, talk to her in her mother's tent.
As a reward, you'll get a red keycard for the Vault 15 elevator, and you'll be able to talk to Zeke, the "leader" of the squatters.