Update the chat example to publish messages on the websocket connection

I think the chat example would be a lot more valuable if the messages were published via the websocket connection instead of as separate HTTP request. I'm trying to migrate from gorilla/websockets but having a hard time figuring out how to both read from and write to a client from different threads. If not publishing the messages themselves, maybe a "typing" indicator when a user is typing in the input? Anything that demonstrates concurrent full duplex communication over websockets really.