This article will help contextualize how to cite AI in Chicago/Turabian: https://www.chicagomanualofstyle.org/qanda/data/faq/topics/Documentation/faq0422.html
Taken from https://www.chicagomanualofstyle.org/qanda/data/faq/topics/Documentation/faq0422.html
The Chicago Manual of Style says that a numbered footnote or endnote for AI should look like this:
1. Text generated by ChatGPT, OpenAI, March 7, 2023, https://chat.openai.com/chat.
"ChatGPT" is considered the author.
"OpenAI" is considered the publisher/sponsor.
"March 7, 2023" is the date the text was generated.
"https://chat.openai.com/chat" is the url where the AI tool is found.
If the prompt you used with AI isn't included in your paper, include it in the note:
1. ChatGPT, response to "Explain how to make pizza dough from common household ingredients," OpenAI, March 7, 2023.
The URL isn't included in this exampled because there is no way to generate a URL that would take your reader to the original ChatGPT question.
Don't cite your AI response in your bibliography or reference list unless you can get the exact link using a browser extension--just include your citations in footnotes or endnotes.