Two stamp collectors have completed a grown-up, multi-million dollar version of the playground swap, to finish an unparalleled compilation.
There are only two Z Grills in existence
The coup by Bill Gross, a US financier known as the "Bond King", means he has the only complete set of US 19th Century stamps in existence.
He finally landed his "Holy Grail" - an 1868 one cent "Z Grill" stamp - after years of trying.
In return he gave up the unique stamps he recently bought for $2.97m (£1.67m).
He handed over the block of four "Inverted Jenny" stamps to Donald Sundman, president of the Mystic Stamp Company.
"It is truly the biggest event in the past 100 years. [The Z Grill] is like the Holy Grail of stampdom," said Charles Shreve, president of Shreves Philatelic Galleries, who represented Mr Gross at the swap.
The printing block number makes the Inverted Jennys unique
Mr Gross needed the Z Grill to complete the first comprehensive set of US 19th Century stamps - something not even the US National Postal Museum has achieved.
There are only two Z Grills in existence. Mr Gross first tried to buy this example in 1998, but was outbid by Mr Sundman, who paid $935,000.
The blue Z Grill features Benjamin Franklin and is named after the experimental security grill on the back.
The swap implicitly gives it the same $3m value as the four Jennys - making it the most expensive single stamp ever.
The 1918 Inverted Jennys are so-called because they feature a Curtiss JN-4 biplane - known as a Jenny - mistakenly printed upside down.
Donald Sundman (left) admitted to "seller's remorse"
This example of the rare stamps is unique because it has the printing block number - also upside down - in the bottom left corner.
Mr Gross paid the world record price for the Jennys only two weeks ago, specifically in order to offer the swap.
Mr Sundman, wearing a tie depicting the Inverted Jenny stamp, admitted to "a serious case of seller's remorse" after handing over his treasured item.
"I bought the Z Grill because it was the rarest stamp in the world. But I get a wonderful item in exchange," he said.