Will AppleCare pay for a new charger?

Apple will replace components that failed where the failure was not caused by accidental damage. For any specific device only Apple can answer. By "charger" do you mean the thingy that plugs into the wall (correctly called a USB power source) or the cable that connects that thingy to the phone (correctly called a Lightning cable)? The "charger" is inside the phone; it isn't either of these items.