I've read quite a few posters (actually quite a lot!) that have reported that this was fixed out of warranty - and one or two people who were told no.
Technically - and this was trotted out by some Apple employees to people who first complained - Applecare didn't cover this as it was a "cosmetic" problem, which the warranty doesn't cover. Happily though, this seemed to stop as an excuse not to repair.
I think one reason so many people reported this being fixed out of warranty was that Apple released this was a design/manufacturing flaw (as per davidjearly's excellent post) and telling people to get lost was counterproductive.
There's a few (pretty old) threads about this, so if you can access these through a search you might get some useful info.
Personally, I think you've got a very good chance of getting this fixed - but as you've got a bit of drive to the store, maybe give them a call first.