You know... "chat" is a funny word.
It's like "cat" and also like "hat." I wonder if that means anything about where the word originally came from...
I bet there were ones cats who wore hats, and they loved talking all the time... so everyone called them talkative kitties with head garments. And then they thought better of it, and thought up a shorter name for kitties with head garments. cats with hats... or chats. And since they talked so much, they became known for their talking, and then everyone called talking chatting.