Linden Lab Official:Billing FAQ
General billing issues
American Express
If you're an American Express customer, be happy: American Express is pretty vigilant about guarding your money.
If you're planning to purchase land or L$ through Linden Lab with an American Express card, you should first call American Express and authorize an open billing agreement with Linden Lab. Once American Express has enabled it, you should be able to use your American Express card to buy land or L$.