My Girlfriend Is Smart

The blog Agoraphilia came up with this puzzle:

Using only a coin, how can you generate a probability equal to exactly one-third?

Here’s more context, if you feel the need for it:

Suppose you want to vacation at the beach, mountains, or desert. You want to choose your destination randomly, with equal chances for all three outcomes. Your only randomization device is a coin. What should you do?

Lauren and I talked about this for a while last night. I came up with some simple-minded ideas, but she came up with The Answer (or at least the most "elegant" Answer). Apparently recognizing infinite series isn't in my skill set. I'll live, I guess.