This Sunday marks the anniversary of the Aug. 5, 1962, death of Marilyn Monroe, after a barbiturate overdose in her home in the exclusive Brentwood neighborhood of Los Angeles.

Her sudden death at just 36 years old shocked the nation — in part because just three months prior she had given one of her most famous performances. Decked out in a skin-tight, nude-colored dress, she sang “Happy Birthday” to President John F. Kennedy, who was turning 45 later that month, at a rally at Madison Square Garden on May 19, 1962.

The performance remains a cultural touchstone decades later, and is also noteworthy because that event produced what is considered the only known photograph of Monroe and Kennedy together.

The image, shown here, was taken that night at an after-party at the Manhattan townhouse of Hollywood exec Arthur Krim, by official White House photographer Cecil Stoughton. A print of that image is now for sale, which the auction house Lelands says it was discovered after Stoughton died in 2008; Lelands claims it could be the only surviving version of the photo that Stoughton printed himself from the original negative. (Another version of the photo is part of the LIFE Images Collection.)

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Also pictured are the President’s brother, Attorney General Robert F. Kennedy, on the viewer’s left, and Harry Belafonte, who sang “Michael Row the Boat Ashore” that night, in the center back. The bespectacled smiling man on the right is the historian Arthur Schlesinger, Jr., who admitted later that he was indeed as starstruck as he looks. Monroe had also brought her ex-father-in-law Isidore Miller, playwright Arthur Miller’s father, to meet the President that night. “I thought this would be one of the biggest things in his life” as an “immigrant,” a 1964 LIFE magazine feature reported her saying.

“[I]t was Marilyn who was the hit of the evening,” according to TIME’s recap of the concert in 1962. “Kennedy plainly meant it when he said, ‘I can now retire from politics after having had Happy Birthday sung to me in such a sweet, wholesome way.'”

The performance added to rumors that both Kennedy brothers were having affairs with the actor. Among the JFK files released to the public last year was the FBI’s warning to Bobby Kennedy about an upcoming book that was going to say the two had an affair. “It was pretty clear that Marilyn had had sexual relations with both Bobby and Jack,” James Spada, one of her biographers, told People on the 50th anniversary of her death. (Any claims that the brothers had a role in her death, he clarified, were unsubstantiated.)

According to another biographer, Donald Spoto, Monroe and JFK met four times between October 1961 and August 1962. Their only “sexual encounter” is believed to have taken place two months before the concert in a bedroom at Bing Crosby’s house on Mar. 24, 1962, her masseur Ralph Roberts has said.

So, while rumors of their affair may have ramped up after her performance at Madison Square Garden, their interest in each other may have been winding down at that point, Roberts has claimed. Referring to their March encounter, he said, “Marilyn gave me the impression that it was not a major event for either of them: it happened once, that weekend, and that was that.”

And yet, especially given Monroe’s death and Kennedy’s assassination not too long after, the idea of their relationship still holds its grip on many Americans’ imaginations.

Bidding for the photo on Lelands.com ends Aug. 17.

Write to Olivia B. Waxman at olivia.waxman@time.com.