According to The Chicago Manual of Style, like personal communications (see 14.111) and social media posts (see 14.106), AI conversations are not normally cited in the bibliography or reference list. They should be cited in the text where they occur, or in a note, whether cited or paraphrased.
Include the following information in the note or reference: author, version number, publisher/developer, date, and URL.
If the AI text has been adapted, acknowledge that in the text or note. A prompt may be included in the text or the note, and multiple prompts can be summarized.
If the AI conversation is included in the reference list, cite under the name of the publisher/developer, and include a publicly available URL.
In-text
This cake recipe was generated on October 31, 2023, by ChatGPT-3.5.
Example adapted from 14.112: Citing AI-Generated Content.