I just asked this question on Wednesday with my AT&T Store, and they said all you have to do is go in and ask. I was more curious about switching to a micro-sim, but it'll go both ways.
Yes, I've picked up over a dozen from different AT&T stores. However in a couple of my experiences I had to shell out $15-30 in order to get a new one. Whether it was legitimate or not I didn't care.
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It really depends who you ask. Some reps would just give you one, some will try to charge you. For the short term, just go to ATT and ask for a new one for your phone. For the long term, I suggest that you order some SIM Adapters on eBay, this is what I used to switch between the iPhone 4 and the Captivate for a short while.