It was 2001 and the North Korean leader toured the country for three weeks. Accompanying him was Konstantin Pulikovsky, a respected Russian diplomat who, as the story goes, took the rare opportunity with one of the world's most withdrawn leaders to talk about family.
Kim is believed to have had seven children. His youngest son and future successor, Kim Jong Un, was in his mid-teens at the time. It was only several years later that the North Korean leader's health would begin to fail him, and it is not clear if he had begun to think about the legacy and how to keep the family dynasty going.
So when Pulikovsky asked about the children, Kim spoke highly of her two daughters.
Michael Madden, an expert on North Korea's management who runs a website on the subject and is a government consultant, said he repeated that anecdote many times over the years when asked about the Kim family. The story has been repeated in various media and academic reports several times since 2001, but CNN could not independently confirm it.
"Kim Jong Il loved his sons, but didn't necessarily have a high opinion of what they were doing with life," Madden said.
However, Kim Jong Il may think it would be a tough seller to name a woman as the next North Korean leader – especially with several sons available.
North Korea is a notorious patriarchal country, where women are expected to be conscientious and subordinate wives and prickly mothers before anything else. Defenders say misogyny, gender discrimination and sexual violence are widespread.
"It's a base culture with only very strong, traditional patriarchal gender norms and female power," said Sokeel Park, director of research and strategy for Liberty in North Korea, a human rights group that assists shoppers.
Experts say that if something should happen to him before his young children are old enough to take over, Kim Yo Jong could be the safest and most likely heir.
If she succeeded Kim, It would put a woman at the center of one of the most repressive regimes on the planet.
The Korean Peninsula is not an easy place to be a woman.
North Korea is hardly the bastion of equality that Kim Il Sung promised would be achieved through economic liberation.
While women are an important part of the workforce, and drivers of the limited private markets in the country – since all men have jobs assigned by the state – female shoppers say they still face widespread discrimination. Furthermore, they lack the professional and social opportunities of their male colleagues.
"Women must always be modest," said Nara Kang, who left North Korea in 2015 and now lives in the South. "Men hold the purse strings many times, and men have all social status."
Jean Lee, an Associated Press reporter who opened the Pyongyang Public Service Office in 2012, said she has endured "incredible sexism in both countries."
"My female North Korean counterparts had the same complaints as my female South Korean counterparts: that they were expected to do their job all day and still take care of all the cooking and cleaning at home," said Lee, who is now director of Hyundai Motor Vehicles. Korea Foundation Center for Korean History and Public Policy at the Woodrow Wilson Center in Washington, DC.
"To be honest, neither Korea, North nor South is a great place to be a woman."
But the south has one calling card: it has had a female leader.
Park Geun-hye broke South Korea's highest glass ceiling in 2015 and became the country's first elected female president.
Madden, the North Korean leadership expert, believes that even though Park's tenure ended in scandal, she proved that a woman can be accepted as a leader in Korea – north or south.
"North Korea has a 70-year history of women being very close to the center of power, of being influential in North Korea's decision-making processes," he said.
"South Korea already broke the shape of the peninsula."
Kang, the defender, is not so sure. When asked if she lived in North Korea imagining it could be a female supreme leader, Kang replied incredulously.
"Oh no," she said. "I can't even imagine. Can't even dream."
An unbreakable bond
But Kim Yo Jong was the one who really made history. She became the first member of North Korea's ruling family to go south of the 38th parallel since 1953, when the Korean War actually ended (the war is still technically ongoing because the fighting parties signed a ceasefire, not a treaty.)
Experts knew Kim Yo Jong was one of the top executives' top aides and confidants. As Deputy Director of the Labor Party's propaganda and agitation department, she was responsible for creating her brother's public image and messages.
But the year before her visit to South Korea, she had also joined the country's Politburo – the senior body of the North Korean government – as an alternative member, adding another important title to her resume.
But average South Koreans knew little else about her, and the mystery sparked curiosity. People were fascinated by this seemingly urban envoy from what is often portrayed as a backward country, representing a leader who at that time had not traveled abroad since he took power.
As governor of the South Korean province where the Olympics were held, Choi Moon soon met Kim Yo Jong. He described her as "very calm and self-possessed", a woman with "very few words" but who speaks precisely and directly.
During the tour, Kim Yo Jong cheered on the inter-Korean hockey team and took in the opening ceremonies with South Korean President Moon Jae-in and US Vice President Mike Pence, who chose not to shake hands. She was photographed watching events and performances, smiling and looking to get along well with her hosts. The press even resembled a North Korean Ivanka Trump.
It became a masterstroke in public relations by one of North Korea's best propagandists.
She put a human face on a regime that the Trump administration at the time was trying to punish as a pariah state and nuclear renegade. And she did while also laying the foundation for his brother's diplomatic push, which would see him become the first North Korean leader to ever meet face to face with a sitting US president.
The visit turned out not only to be Kim Yo Jong's upcoming party to the world; she showed how good she was at a role she had spent much of her life preparing for.
Further details of her childhood are scarce.
In Switzerland, the adults are around Kim Yo Jong and Kim Jong Un tried to give the children a normal life, but they all had to keep so many things secret – their real identities, their wealth and their mother's ongoing treatment for terminal breast cancer at the time.
The Kim siblings shared a childhood that was remarkable, but uniquely lonely and lonely. It was an experience that few can empathize with. Kim Jong Il would have been the one who decided to raise them together, and experts like Madden believe it may have been on purpose.
"As they get older and become more aware of the circumstances they grew up with, it's a pretty tough reality to face. And of course, it's a hard reality they meet," Madden said.
"Nobody can relate to it. Kim Yo Jong and Kim Jong Un, I think they have a relationship that is impossible to break."
Given the intense secrecy surrounding the Kim family, we may never know how difficult it was for Kim Yo Jong to transition from gender discrimination to rise to the top of North Korea's political hierarchy.
But Kim Yo Jong is no ordinary woman.
Kim Jong Il had more children than Jong Un and Yo Jong, and the siblings still have live aunts, uncles and siblings. But Madden says that Yo Jong and Jong Un are the only two living in state media as the true heirs to Kim Il Sung's "Paektu bloodline," a reference to the mythical mountain on North Korea's border with China.
"There is no other legitimate descendant of Kim Il Sung when it comes to North Korea's political culture," Madden said.
If Kim Jong Il wanted her near power, it is now clear that the deceased North Korean leader got his wish.
All the experts CNN spoke to for this story agreed with the theory that being a woman will not hold Kim Yo Jong back. But it has more to do with her status than changing gender dynamics in North Korea.
"Gender, I think, is not prohibitive," said Liberty Park, North Korea. "Obviously it would be a first, and it's a patriarchal system and so on, but I think the Paektu bloodline, the Kim bloodline, overrides that."
Lee, the former AP bureau chief in Pyongayng, said she also believes her legacy "is more important to Kim's than gender."
"For many years, Korea watchers have said that North Korea would not accept a woman," she said.
"I have said for many years that it is quite possible that the next leader in North Korea will become a woman – as long as she is the best Kim for the role."
CNN's Nathan Hodge, Sophie Jeong, Yoko Wakatsuki and Paula Hancocks contributed to the reporting