I'm not an expert on Credit Card theft, but this happened to my GF in New York City two years ago. The card never left her purse as I paid for everything, but on one occasion she had to show ID and we think someone was able to take a photo of the front of the card when her wallet was open to retrieve her ID. That was the only time the card was visible during our trip.

Didn't know about the smart chip.

Good luck,

VVHT