The ghosts of the Vietnam War haunt this week’s summit between Donald Trump and Kim Jong Un, the North Korean leader formerly known as “Rocket Man.” Especially since the talks are taking place in Hanoi and the specter of a Nobel Peace Prize is now hovering in the background.

At a White House press conference earlier this month, Mr. Trump said that Shinzo Abe, Japan’s prime minister, had given him “the most beautiful copy” of a letter to the Norwegian Nobel Committee. Mr. Trump said Mr. Abe had nominated him for his work to bring peace to the Korean Peninsula. South Korean President Moon Jae-in also believes Mr. Trump worthy of the prize. So do at least two Norwegian lawmakers, who nominated Mr. Trump for the prize last year.

United Press International reports that North Korean state media is promoting a peace prize for Mr. Kim as well. And if Mr. Trump is awarded the Nobel, it’s likely he would share it with Mr. Kim—in the same way that Henry Kissinger shared the 1973 prize with his Vietnamese counterpart, Le Duc Tho. The two men had negotiated the Paris Peace Accords that year.

But the history here is a cautionary tale. Recall that when the 1973 prize was announced, it provoked global outrage—against Mr. Kissinger. Two Nobel committee members resigned. Mr. Kissinger didn’t go to Oslo to deliver the customary acceptance speech for fear of massive demonstrations.

This is the way of the world. If history does repeat itself with a Trump-Kim Nobel, we are likely to find similar outrage—and from people who have more moral qualms about Mr. Trump than about Mr. Kim.