Yup, had the same problem with my iPhone 4, about 1 day after getting it.
Reset Sim card - didn't fix it
Got new Sim card from AT&T store - didn't fix it
Apple "Genius" reviewed problem, did restore, saw it was hardware problem, replaced phone
Now I'm waiting to see if replacement phone exhibits same problem. It's only been 1 day, so I'm cautiously optimistic.
"Genius" said he has seen a couple with the same hardware issue. Said it is due to sim contact problem within phone.
Still, not a good start for this new iPhone customer, who already waited a week for mine to come in via "priority list" - but, I'll cut them some slack due to the large quantity getting sent out (there will always be a few bad ones, and the new customers likely end up with the bad ones, right?)