I got a call from someone saying that their card was fraudulently charged. Would I just simply credit their money back to the card or should I tell them to contact their credit card company directly?

I know if they contact their card company I'll get hit with a chargeback, but obviously this person's card got compromised and someone could be using their card at some other company. What would be the best way of handling this?

I would recommend doing three things, #1--issue the refund to avoid a chargeback, #2--advise the alleged victim to contact their credit card company, #3--contact the credit card company yourself.

This of course assumes you aren't willing to fight the chargeback, etc....

ExtremeIS is correct. You should also contact your cc processor first. Let them know you have no issues in giving them a refund. But you need to let them know so it is documented in case it comes back to bite you.

Issue an immediate credit to the cardholder and explain to them that someone has compromised their credit card but that you are removing the charge that came from your company.

Do NOT have customers contact their bank to get a refund or else it will become a chargeback for you. Just issue the credit and then let them know to contact the other merchants who have been charging their cards.

Only as a last resort, should they have to charge anything back. Otherwise, a list of merchants will become victims along with the cardholder.