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I had to send them my full payment before they started production, a couple of months before I got the car. In the long term, it wasn't a big deal; Tesla's got a good track record of actually delivering (now that they've got the production going. It was a different story in 2008.)
I made the last portion of payment at the time of delivery. I believe I could have paid only the $9900 deposit up front and then the balance on delivery day. But I was taking delivery at the Seattle store.