Help with PlayerAdded Event?

I'm trying to create a Chat log thing with this script:

game.Players.PlayerAdded:connect(function(Player)
	Player.Chatted:connect(function(Message)
		print(Player,":",Message)
		end)
end)

But I have a question will this script only fire on just the newly added player and have control on all of other players?

Example of what I mean:

Player1 joins the sever and chats it will fire the chat event

Player2 joins the server and chats it will fire the chat event,but will it still fire for Player1?