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An arn was a creature about the size of two human thumbs, with teeth and poisonous claws, which was used in a punishment by the Rhodians. When they would release it into the brains of those to be punished, it would burrow itself inside. The creatures would telepathically link its host with a particular Rhodian, and then they would be their slave.
At least in Miss Quill's case, if she used a weapon other than her own hands, the arn would kill her; if she failed to protect Charlie, the arn would kill her; if she attempted to remove the arn, it would kill her. She was also not allowed to tell him lies. (TV: For Tonight We Might Die)
Dorothea Ames and the Governors were able to remove the arn from Miss Quill's head, leaving her with a scar over her eye. (TV: Detained)