I called the credit card company. The rep didn't seem too bothered by the fact that there was an unauthorized charge on my account. I guess they hear it pretty often...

He said the merchant was some sort of travel booking company. He's going to mail me some forms to fill out and send back to them. It will take 30 to 60 days.

This really sucks because it was a substantial amount of money and it brought my available credit down to almost nothing.

Thanks to everyone who responded.

Imago