The oil giant is not identifying the business, citing confidentiality but acknowledges that it lobbied for the $10 million settlement.
Latest records show that roughly 91,000 people and businesses had filed for final settlements, but the fund's administrator Kenneth Feinberg said those checks won't start rolling out until February at the earliest.
Thousands of people have received some money to tide them over until a final settlement amount is offered, but only that one listed as paid on the facility's website has so far received a check.
Feinberg has faced repeated criticism from lawmakers, plaintiffs attorneys and claimants who complain about a lack of transparency and independence from BP, as well as claims being shortchanged and paid too slowly, or not at all.
His law firm had been receiving $850,000 a month from BP for its work. Feinberg is currently negotiating with BP over a new payment structure to run the fund through August 2013. Any money left over from the $20 billion is expected to be returned to BP.
The Associated Press contributed to this report.