Because other readers/researchers can't retrieve your chat transcript, it's not going to be cited the same way that work by an author would be.
In general, credit the fact that AI was used, and when, and which (ChatGPT, etc.) and, as per the APA, the "inventor of the algorithm."
Again, it's very plausible that ChatGPT and other AI tools will generate references that don't exist in the real world. It's crucual that students check any references given by AI and if you do find good references, it's very possible that examining these resources will be a better idea than using the contents of a chat session for research.
Because the implications for research are rapidly developing, there can be some standards for citations that will change. Below are some general guidelines for citing and using responses from a ChatGPT session, but these are subject to change.
Some researchers are concerned about copyright. Currently, the Federal Government will not copyright AI generated work, stating that copyrighting "can protect only material that is the product of human creativity."
Don't treat the Chat as an author.
Do include the prompt, container (ChatGPT or something else), date, version, and location in your works cited. Paraphrase the information you're using in your writing. Here's an example from the MLA website: