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AMEX never forgets. They will most definitely still have that record internally.
However, since you did, in fact, pay it off eventually, IMO it shouldn't hurt you with your chances for new credit with them. They even offer secured credit (which later converts to unsecured credit) to folks who didn't pay them off in the past, but are willing to do so now. Search these boards for the AMEX Oasis program.
Good luck, BarnabysMom!
Edited: not sure I'm phrasing this right...
"They even offer secured credit (which later converts to unsecured credit)"
Perhaps someone else here can do better with this...