As Neal goes through his mail, Mozzie says he's talked to everyone who would or could know about the music box. Nothing's coming up. Neal has received another postcard from an anonymous chess opponent, but this one is different from the previous ones. It isn't postmarked, and it's a picture postcard of the New York Museum of Natural History. Neal takes a miniature chessboard from the bookshelf and makes the move written on the card. Then he realizes his opponent is "Keller", and they've been playing a game they didn't finish long ago.
Neal is researching a recent theft at the museum when Burke arrives at the office. The thief stole some interesting items: antique cork duck decoys from the storeroom, wax-sealed supply lists, and French soil samples that belonged to a famous botanist. The NYPD already has a suspect, Manuel Campos. He's just been released on bail.
As they walk down the sidewalk toward Campos' home, Burke asks Neal what's going on. Whatever it is, Campos clearly isn't the mastermind. Neal says he has a theory. They're about to cross the street when a speeding car races past, hits a man down the block and flees. The hit-and-run victim is Campos, who dies later at the hospital.
Neal tells Burke the responsible party is Matthew Keller, a blue-collar version of himself. Keller has been on both the Bureau's radar and Interpol's, but he's never been caught. Among his international heists is a daring theft of Krugerrands from Stockholm Airport. Neal and Keller met early in their criminal careers, and have been rivals of a sort ever since. If Keller is involved, he probably bailed Campos out in order to get rid of him.
The museum theft is related to an old bet Neal and Keller made: to counterfeit a bottle of wine given to Benjamin Franklin by Marie Antoinette. It's rumored to be in private hands, but it's never gone to auction. The wine cannot be counterfeited, hence the challenge. Burke says he doesn't care about the rivalry, only about nailing Keller if he killed Campos over the Franklin bottle.
Burke interviews Sir Roland Cattigan, a wine expert from Weatherby's auction house. Cattigan tells him the Franklin bottle will be included in their auction taking place later that week. Asked why the Bureau wants to know who's selling it, Burke replies that the wine is a forgery. After initially declining to identify the seller, Cattigan falls for a bluff and tells Burke the anonymous seller's broker is Grace Quinn.
Quinn runs an upscale wine cellar. To find out if she knows Keller, Neal visits her as the representative of a client who's interested in the Franklin bottle. Quinn invites Neal to bring his client to a private wine tasting she's hosting. He sweet-talks her into giving him a tour of the cellar, including its state-of-the-art vault. Eventually he maneuvers her into confirming that Keller is the anonymous seller of the Franklin bottle. Neal then sees a postcard sticking out of a history book on a table. The card marks a page about an old tavern which used to be on Water Street. On the card is a message: "8 pm".
Burke learns from Interpol that Keller is a marked man. His Stockholm Airport heist was financed by the Russian mob, but Keller never gave them their cut of the take. He must be planning to pay them with the sale proceeds from the Franklin bottle.
Keller wants to carry out the old bet with Neal. He gives Neal the necessary period wine bottle to start, and 10 days to play the game. Neal accepts the challenge in order to bring down Keller for murdering Campos.
Burke lectures Neal for not clearing the meeting with him first, notwithstanding that they have no evidence against the smart-operating Keller. Weatherby's received Keller's Franklin bottle that morning and locked it in a vault. Neal proposes that he submit a fake bottle, which will force the auction house to run a cesium test. Just as the Franklin bottle can't be counterfeited, the cesium test can't be beaten. When both bottles fail the test, the Bureau can charge Keller with fraud. It's not murder, but it's a start.
Neal is short one item for his bottle, period beeswax. Quinn has some wine bottles from the appropriate era in her vault. To get to it, Neal attends the wine tasting with Burke posing as his client. Burke talks Quinn into showing him the vault, and surreptitiously tapes the door bolt open. A few minutes later Neal goes in after the beeswax.
Back at the party Burke sees Quinn and another guest head toward the vault. He follows and tries to stall them, and the guest sends Quinn to get him another glass of wine. After Burke and the guest talk for a few moments, Neal comes out and formally introduces Burke to Matthew Keller. The egotistical Keller says a few more taunting words before taking his leave of an infuriated Burke and Neal.
Hughes informs Burke that Weatherby's has closed the auction to new entries. Burke researches the auction house's history and finds another way in. The auction is in full swing when Burke and Neal arrive, but Keller's not there. He must be watching from nearby.
Cattigan again refuses to admit Neal's bottle to the auction, and Burke plays his ace. The previous year Weatherby's sold six bottles of a 1947 wine at $50,000 each. However, the vineyard produced only five bottles of that wine that year. On behalf of her client Quinn agrees to the cesium test. Burke also asks Cattigan for the IP addresses of everyone watching the auction on Weatherby's Internet feed. While the test is being run, Cruz tracks down the addresses and traces one of them to a nearby parking garage.
To Burke and Neal's surprise, Keller's bottle is genuine. Then they realize why: Keller had the real bottle all along. He challenged Neal to carry out their old bet in order to surround the bottle with controversy, thus driving up the price. Keller has played them masterfully. Burke takes off to find him while Neal remains at the auction to try and stall the bidding.
Mozzie joins Neal at Weatherby's after confirming the Russians are in town, and that a man named Sergei expects Keller to pay up the moment the auction is finished. In the parking garage Burke and Cruz find an empty car with a laptop tapped into the auction. Keller saw them coming and escaped just before the Bureau sealed off the place.
The bidding on the bottle reaches $800,000. At Neal's instruction, Mozzie bids $1 million and wins. Burke tracks the fleeing Keller on traffic cameras. Neal catches up with his rival at the waterfront, where Sergei is waiting in a helicopter. After acknowledging Keller's genius, Neal offers him the opportunity to make a full confession to the museum robbery, Manuel Campos' murder, and anything else Keller may want to throw in.
Keller turns away and heads toward the helicopter. Neal then reveals that he was the winning bidder, but he doesn't have $1 million handy. Weatherby's has given him a week to get the money together. Burke arrives and adds that he's launching a full-fledged federal investigation into the bottle which could drag on forever. Realizing what will happen if he gets into the helicopter with Sergei, Keller opts to accept Neal's offer instead. Neal broke out of prison; perhaps it's Keller's turn to accept the challenge.
Later, Mozzie tells Neal that there's suddenly a lot of chatter about the music box. He suggests that Neal talk to Alex Hunter. Neal says she won't talk to him as long as he's working for the Bureau. Mozzie replies, "Make it worth her while."