"Thanks for the chat" is correct and usable in written English. You can use it in an email or in social media as a polite way to end a conversation. For example: It was great catching up with you. Thanks for the chat!.
Small Talk isn't sure we've got that much time on our hands Sergio, but thanks for the chat.
QUESTION FROM GUEST: I loved "Paris to the Moon" — thanks for the chat ADAM GOPNIK: A nicely generous note to end on.
What the law doesn't say is what will happen if, once consulted, the religious group says "thanks for the chat but we're not handing over the school".
Thanks for the chat, David.
Thanks for the chat and for your questions.
Thanks for the chat and for the review, I've got to go and pick up the kids now.
MR: José, thanks sir for the chat, I appreciate it, all the best.
Thanks for joining the chat.
Well, thanks again for chatting to us, and thanks for the music.
Dave: Well, first, it's great to chat with you, Tom, and thanks for the opportunity.
QUESTION FROM ANTHONY IN UK: Mr. Filkins, thanks for doing this chat.
Ludwig does not simply clarify my doubts with English writing, it enlightens my writing with new possibilities
Simone Ivan Conte
Software Engineer at Adobe, UK