While it's possible the port is bad, it would be unusual for it to fail this soon, unless it was somehow abused (picking the phone up by the cable, for example). A few things you can try to diagnose the problem:
if you have another micro USB cable, try it with the OEM charger. The cable Samsung ships is notoriously cheap. If a different cable solves the problem, you have your answer.
Try the OEM cable (and a different cable, if you have one) plugged into a computer's USB port instead of the charger. Use a USB port on the computer, not one on a USB hub. Does that make a difference?
Use any other micro-USB charger. They all put out 5 volts, and as long as it puts out at least 700mA it should be fine. Note that chargers designed for iPhones and iPods will charge more slowly than other chargers, but should still be better than what you describe.