What would you be deleting though? Do you just want to hide some chats so they don't get in the way when scrolling through other chats? We could put deleted user chats at the bottom or something.
Deleting wouldn't really do anything if the other person is still a user because you can't delete their ability to view the messages, as that would violate their right to the conversation. You can delete your individual messages of course.
I suppose we could allow deleting or hiding a chat if the other user is deleted. If we allow deletions though, then the conversation would be gone forever so you'd never be able to go back and view it. Would a hide button be better?