I'm own a mail order business that takes credit cards. About three times a year I get a call from a customer describing the exact thing you've experienced. In every case I clammered around to investigate as I know the customer is very concerned, and in every case I find that we only charged his card once. Each time I explain this to the customer who probably thinks I'm making it all up. And in every case, it turns out the customer is always charged just once when it's all said and done.
I could go into details of HOW and WHY this happens, but its long and boring. The long and short of it is that a communication error probably caused it. If it makes you feel any better, most merchant systems literally will not allow them to charge the same amount to your card a second time in the same business day, though this is a configuration option that can be changed. I would think most mail order merchants would keep the default so they can't accidentally double charge a customer.
If it were me, I'd call my card company now, and depending on what they say call CSUSA on Monday. But I'm willing to bet it will all automatically resolve itself within three business days. If it was a particularly large order and you will need to be using your card, though, you might want to get it resolved sooner than later as it could cause another transaction somewhere else to get declined for no apparent reason (if the second charge uses up the rest of your available credit).
I've got a feeling this happens far more than anyone realizes, it's just that it's rare a customer happens to log in at the right time to see it happen. All I can say is that in the old days when it was all done on paper, it would take tens days for a problem like this to get resolved.
I hope it all works out without too much trouble for you.
-Matt