Years ago one of my cards got hit online by a lucky hacker with a list of that bank's credit card numbers and security codes to the tune of $7,800 the bank ate it.
I had one card burned locally, at Target 7 years ago, cloned or their POS terminal hacked. The fraud was a bit little over $1,100.
Now I only use debit cards on my "public accounts" that rarely have more than $1,500 in them that is exposed.
I had a fraudulent charge of $535 a few years ago -- my bank took an affidavit from me, replaced the card with a new one and in the end charged back the processor.
Just dispute the charges and complete the bank's affidavit -- they will issue you a new card and chargeback the merchant or processor(s). I imagine that the new cards' bank fraud department will close the account if fraudulently opened without much hassle.
Credit Card with Chips | Chip Card | Visa USA
I am opening bank accounts this week at a couple of Internet banks that have cards with these chips so I can use the cards outside of the USA where only these EMV -- which stands for Europay, MasterCard and Visa -- is a global standard for cards equipped with computer chips. They as Sloowly replacing credit cards with EMV chips at some US banks.