I have no idea if that is technically possible, but could a lightweight bitcoin client be integrated in a mastercard chip?
Essentially yes, but they can do something far more interesting than just a client - Mastercard or Visa have the trust and knowhow required to make that smartcard chip guarantee that it will A: keep the private keys secure, and B: never double-spend. Thus allowing for very safe zero-confirmation transactions, provided they come from such a card.
They can also go the next step beyond that, and make the whole system off-chain as well, allowing Bitcoin card holders to avoid blockchain transaction fees entirely. Of course this can be done as a hybrid system, with the card using either method to make a payment, depending on the circumstances.
There is no reason to expect any of Visa, Mastercard, PayPal etc. to stay out of Bitcoin forever. With the 1MB blocksize limit they can all offer off-chain transaction services, and at the same time, if the limit is raised they can also all offer zero-conf transaction services, as well as run the expensive validating nodes that will be required and mining pools.