I have the same exact problem, and I even made a post about it a week or so ago. It drives me insane, because I've kept my iPhone inside of a case whenever it is not in use and I've been ridiculously careful with it. Heck, I've been storing it inside of a soft rubber case and have been placing the whole thing inside of a soft case.
I really have no idea why I am getting scratches on the chrome border. It is unfortunate that the rest of the iPhone is so scratch resistant, but Apple just had to include the classic "iPod super scratch material".
I contacted one of the scratch remover companies about using their product on the border and they stated that they had received some positive feedback indicating that it does work well on the chrome border. However, I am a bit apprehensive about using the cleaner on the iPhone since it does contain a mild abrasive.
does it make me a bad person that I don't care if my phone is scratched? I ordered the sweet skin you see in my avatar. So I'll never really have to worry about scratches being visible. I've dropped my iPhone 5 times. sure it sucks now, but when that skin gets here, I'll forget they're there.
I'm going to try some Chrome Polish if mine gets any more scratches. It just has a few very small ones from the Belkin clear case I used over that first weekend. Returned it for full refund. Waiting on my best skins ever to arrive tomorrow or early nest week, but realize they don't cover the chrome bezel.