For Chicago, it is recommended that you cite ChatGPT for any generated text which you have used (whether paraphrased or directly quoted). For other uses of the software, you should acknowledge the software in the text of your document (e.g. "ChatGPT was used to compile a list of Regency era poets.")
To cite text generated by ChatGPT, they offer the following example:
1. Text generated by ChatGPT, March 7, 2023, OpenAI, https://chat.openai.com/chat.
Do not include an entry in the reference list, as the infomation is not retrievable.
Treat in a similar manner to personal communication:
(ChatGPT, March 7, 2023).
Once again, do not include an entry in the rference list.