Using an American credit card in a Tube machine at Heathrow

If I have the time, I'm planning to buy Oyster Cards and seven-day travel cards for my wife and me after we arrive from the States at Heathrow. We won't use them until a week later, but I'm a do-it-ahead kind of guy. However, I understand that the vendor at the airport is a machine, and my American credit card with its chip (not chip and PIN) has failed to work in other places in Europe. Will I encounter the same difficulty with the machine at Heathrow?

We will return to London via rail at Paddington, so I can deal with a human being then, so I do have a reasonable Plan B.