iPhone 5 not charging - faulty wires. Does Apple have to replace it?

I upgraded to the iPhone 5 when it was released, it was delievered a week after the release so I have had it for less than 2 months. I have always had my charger plugged in to the wall or in my laptop, therefore not been misused yet the wiring in the USB (just below the connector for the charging port of the phone) is breaking away and doesn't charge properly unless I wiggle the wire around which I imagine is breaking it further! This started yesterday... so if I were to go in to the Apple store would they be obliged to replace it? I don't think it's right that after less than 2 months my cable is broken already! Help!!