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"Chargeback" is the term used when a customer refuses to pay an item on the credit card bill. It's so named because the charge gets put back on the merchant; each credit card company puts the burden of proof upon the merchant to prove the customer should pay.

In many cases (hotels especially), the cost of proving the customer should pay outweighs the original charge. If you go into a hotel bar and run up a $5 bill, but challenge the item on your credit card bill, the hotel may decide it's cheaper to eat the $5 than to spend $10 having someone search through a pile of receipts looking for the one with your signature. This is becoming less common now that more companies keep digital archives of the receipts that enable fast searching, but still holds mostly true.

"Chargeback" is also used in a business to business (B2B) sense, when the seller agrees that the buyer has a legitimate reason not to pay part or all of the invoice. B2B contracts can be very complicated things, and it is a surprisingly common occurrence for the seller to overlook a special rate the buyer has negotiated. Since all business transactions have to be recorded in the general ledger and balance out, the common practice is to charge the unpaid part of the transaction back to the seller (hence the name chargeback), and then transfer it to the account set up for that contract.