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The results of a ChatGPT "chat" may not be retrievable by other readers. APA Style cites non-retrievable sources as personal communications, but in the case of AI there is no person communicating. Quoting AI is more similar to sharing an algorithm's output, so, credit the author of the algorithm with a reference list entry and the corresponding in-text citation.
Example
When prompted with “Is the left brain right brain divide real or a metaphor?” the ChatGPT-generated text indicated that although the two brain hemispheres are somewhat specialized, “the notation that people can be characterized as ‘left-brained’ or ‘right-brained’ is considered to be an oversimplification and a popular myth” (OpenAI, 2023).
Reference
OpenAI. (2023). ChatGPT (Mar 14 version) [Large language model]. https://chat.openai.com/chat
You may also put the full text of responses (especially long ones) from ChatGPT in an appendix of your paper, so the readers can access the exact text that was generated.
Example
When given a follow-up prompt of “What is a more accurate representation?” the ChatGPT-generated text indicated that “different brain regions work together to support various cognitive processes” and “the functional specialization of different regions can change in response to experience and environmental factors” (OpenAI, 2023; see Appendix A for the full transcript).
Reference
OpenAI. (2023). ChatGPT (Mar 14 version) [Large language model]. https://chat.openai.com/chat
Note: Content adapted from https://apastyle.apa.org/