These English-made dueling pistols, owned by John B. Church, were used in the duel between Alexander Hamilton and Aaron Burr. (JPMorgan Chase Corporate History Program)

Of all the Alexander Hamilton objects being displayed in “Hamilton”-related exhibitions in Washington (the musical opens June 12 at the Kennedy Center), the most fascinating is at the National Postal Museum: the pistol that Aaron Burr used to kill him.

The centerpiece of the Postal Museum's “Alexander Hamilton: Soldier, Secretary, Icon” is a set of flintlock English dueling pistols, made of walnut, brass and gold. They sit alone in a glass case and loom larger than anything else in the room.

Before you ask: No, no one knows which pistol was used by Hamilton and which by Burr in their duel July 11, 1804. Both were the property of Hamilton's brother-in-law John B. Church, who fought his own (nonfatal) duel with Burr in 1799, and they were used in the 1801 duel in which Hamilton's son Phillip was killed. When Burr challenged Hamilton, Hamilton was obliged to choose the method, and he selected Church's pistols.

These are tools for a serious duelist, with weighted barrels and adjustable front and rear sights to improve accuracy. They also have secret hair-triggers, somewhat unbecoming for a gentleman's weapon, which were discovered in the 20th century when the historic guns were disassembled during the process of making reproductions.

Look closely, and you'll see that the two guns don't quite match: One has had its flintlock striking mechanism replaced with a slightly more modern percussion cap system. Church's grandson apparently “upgraded” it for use in the Civil War.

The grimly fascinating weapons — it's hard to forget that one of them, and maybe both, was a murder weapon — are an outlier in the Postal Museum exhibition. Many of the items on display trace Hamilton's military and political career through philatelic materials: stamps showing Revolutionary War battles, letters to other prominent Americans and “free frank” envelopes that Hamilton, as secretary of the Treasury, could send just by signing his name. (Hamilton used this privilege to stay in contact with U.S. Customs officials to keep abreast of imports, exports and the political mood.) One memorable display pairs the first stamps to feature Hamilton, issued in 1870, and the 1794 bust by Italian sculptor Giuseppe Ceracchi that was pictured on them. Hamilton's wife, Eliza, kept a copy of this bust in her home in Washington after his death.

So how did the pistols wind up in the Postal Museum? For curator Daniel Piazza, it was simple: Hamilton's role with the fledgling Post Office Department was worthy of an exhibit at the Postal Museum, and no other Smithsonian museum was planning anything “Hamilton”-related this summer. “I'm the curator of the stamp collection,” Piazza says. “My heart is in the stamps. But you have to have a few other items that will encourage people who might not otherwise come to the Postal Museum to come and see us, too.”

And Piazza knew that the pistols would be a draw, especially since it's the first time they've been shown in Washington. “Being one of the Smithsonian museums that aren't on the Mall, we have to work a little harder,” he says.

The pistols are normally on display in the New York City headquarters of banking giant JPMorgan Chase, though not where the public can see them. “They're our most prized set of artifacts,” says Jean Elliott, the director of JPMorgan Chase's Historical Collection, which has thousands of objects, including the very first Federal Reserve $1 bill and early documents of the Manhattan Company, the bank established by Burr that has grown into JPMorgan Chase over the past two centuries.

Since 1930, when the Bank of the Manhattan Company purchased the pistols from Church's great-granddaughter, they have remained at the bank's headquarters at 270 Park Ave., except for two brief loans to the New-York Historical Society for Hamilton-related exhibits. Earlier this year, JPMorgan Chase announced plans to build a new headquarters in New York, and there has been “a lot of discussion about how we can better share these artifacts,” Elliott says. “We have an opportunity in front of us to change who can see these.”

For the foreseeable future, though, this is the only chance that “Hamilton” — and Hamilton — fans will have to see these remarkable objects. Don't throw away your shot.

Alexander Hamilton: Soldier, Secretary, Icon: at the Smithsonian's National Postal Museum through March 3, 2019. The Hamilton-Burr pistols will be on display through June 24. Free.