The chip, the machines to make the chips, the plastics, the microprocessor, the communications protocols, the error correction, the networking, the programming languages, etc.
If you mean "the notion of a microprocessor", that might well be a US invention, although the particular chip used in the first "smart cards" was, I think, originally developed by Bull, a French company.
The machines to make the chips:
Yes, probably originally developed in the US.
If you mean "the plastics from which credit cards are made", that's probably polyvinyl chloride acetate; PVC was originally a German discovery, although it appears that a US company may have been the first to make it a practical plastic.
However, if PVCA is an enabling technology for smart cards, so are "arabic" numerals, an invention from India; it's as much an enabling technology for "dumb" cards, and, as such, not particularly relevant.
See above, for "the chip">
The communications protocols:
Are you certain that the particular protocols used for chip cards, or EMV cards in particular, were a US invention? The "M" and "V" in "EMV" were US companies, but the "E" stands for "EuroPay", and the protocols might have been based on European protocols used prior to that.
The error correction:
Which particular ECC is used?
To which networking are you referring? The one between the payment terminal and whatever host it talks to?
The programming languages:
OK, what programming languages are used? Pascal had better not be one of them, given that it was a European creation.