I've heard that some sites, including Stack Overflow, have banned AI-generated answers.
Are AI-generated answers, such as those created using ChatGPT, permitted on this site?
Tl;dr No. AI-generated answers are prohibited on GenAI Stack Exchange. Note that this also applies to Tag Wikis. AI-generated content is still prohibited even if is listed as AI-generated.
Answers created by LLMs are generally harmful to the site. They carry a number of significant issues, but the "primary problem is that while the answers which ChatGPT and other generative AI technologies produce have a high rate of being incorrect, they typically look like the answers might be good and the answers are very easy to produce." 
The ease of generating that type of "answer" often results in users posting a large volume of AI-generated answers, and they usually require an SME to determine if the answer is actually wrong.
Note that this doesn't mean you may not include AI-generated content as examples to support your answer - it means that your answer itself must not be AI-generated.
It is acceptable to post AI-generated answers. We shouldn't blindly discriminate against AI. If some AI provides a correct answer, possibly with a few modifications made by a human, then it shouldn't be deleted on the grounds that it was AI-generated. No need to waste human time if some AI can do it. However, if an SE user tends to post incorrect answers, then they should be banned.