“Camp David” stars, from left, Hallie Foote as Rosalynn Carter, Ron Rifkin as Menachem Begin, Khaled Nabawy as Anwar Sadat, and Richard Thomas as Jimmy Carter. (Tony Powell)

A Jew, a Muslim and a devout Christian meet at a camp in rural Maryland. They don’t emerge for 13 days.

It sounds like the beginning of a bad joke, but it’s actually the premise of the play “Camp David,” which had its world premiere at Arena Stage last week. It’s a behind-the-scenes imagining of the 1978 peace negotiations between President Jimmy Carter (played by Emmy winner Richard Thomas), Egyptian President Anwar Sadat (Khaled Nabawy) and Israeli Prime Minister Menachem Begin (Tony winner Ron Rifkin). Famed for its secrecy, the summit gave birth to the Camp David Accords, a treaty that earned Sadat and Begin a shared Nobel Peace Prize and has kept peace between the two Middle Eastern contingents.

The story of how “Camp David” came to be starts not with the playwright, Pulitzer Prize-winning author Lawrence Wright, but with a former member of Carter’s administration. Gerald Rafshoon, who attended the negotiations as Carter’s communications director before pursing a career as a television and film producer, sat on the idea for 35 years.

“Conflict makes great theater,” Rafshoon says. “Historical conflict makes even better theater, because it really happened … I always thought [the Camp David negotiations] would make a good movie.”

But it’s hard to get a movie made, so after the success of “Frost/Nixon” on Broadway, Rafshoon decided to pitch the story as a play. He took his concept to Broadway producer Rocco Landesman, who introduced him to Wright, a renowned playwright and New Yorker reporter.

“It was one of those ideas that I wished I’d thought of myself,” Wright says. “It was one of the great triumphs of 20th-century diplomacy, and yet I don’t think people know … the drama that was taking place within that gated area, where for 13 days those men thrashed out the most durable peace treaty that has ever come out of that region.”

Once Arena Stage signed on as a partner (artistic director Molly Smith says the show is “exactly in the sweet spot of what we do”), Wright approached the play like it was a New Yorker assignment: with heavy research and a determination to do justice to all three men’s perspectives. He and Rafshoon even traveled to Tel Aviv and Jerusalem in Israel and Cairo to interview surviving members of the negotiating teams.

Director Molly Smith, foreground, producer Gerald Rafshoon, center, and playwright Lawrence Wright brought a journalistic approach to Arena’s “Camp David.” (Marvin Joseph/The Washington Post)

Rafshoon’s friendship with Carter and first lady Rosalynn Carter proved a crucial asset — he persuaded both to hand over the diaries they kept during those two weeks at Camp David, which offered insights and details that had been hidden away.

The history books may list three power players at the Camp David table (Carter, Sadat and Begin) but Smith says that version of the story leaves out a “hidden hero”: the first lady. Rosalynn Carter (played in “Camp David” by Hallie Foote) was a sounding board for the president during the talks. In fact, it was her idea to hold the negotiations at the camp, a peaceful place isolated from the outside world and the prying eyes of the press.

During Smith’s research, she joined Rafshoon for a weekend with the Carters in Plains, Ga., where they watched the former president teach Sunday school (that day’s topic was, fittingly, Jesus as a peacemaker) and got to know the couple.

“As [the play’s] director, I was soaking up their relationship — the way in which they listen to each other, the way in which they respond to each other,” Smith says. “[‘Camp David’] is really an opportunity to delve into a long-term, profound relationship between two people … who’ve known each other since childhood.”

The peace agreements that arose from Camp David were never a sure thing — at one point, Carter thought Sadat’s own delegation was going to assassinate Sadat to block a treaty with Israel — and each party made unpopular concessions for the greater good. Wright hopes his take will add nuance to discussions of Middle East politics.

“The Camp David Accords have been called a cold peace,” he says. “It’s an unloved treaty, and yet it’s actually endured. It required compromises on both sides that were painful, but that’s what peacemaking is all about.”

For a story that starts like a bad joke, that’s a pretty profound punch line.

Summer Campers

Every president since Franklin D. Roosevelt has spent time at Camp David. Whether for work or play, the secluded grounds in Maryland have long been a cherished locale.

A Household Name

In 1939, the Works Progress Administration finished building a retreat for federal employees and their families, Camp Hi-Catoctin, about 60 miles northwest of D.C. FDR was the first president to use it as something of a vacation home, a respite from the stresses of Washington that he called the USS Shangri La. Dwight Eisenhower later changed its name to Camp David in honor of his grandson.

Carter Nearly Cuts Camp

When Jimmy Carter took office in 1977, he sold the presidential yacht in a largely symbolic act of budget cutting. He nearly sold Camp David, too, before he’d had a chance to visit. By the end of his term, he was thoroughly convinced of its value.

The Gipper’s Getaway

Ronald Reagan spent more time at the woodsy refuge than any other president: nearly every free weekend, 517 days in total.

No Repeat Performance

Inspired by Carter’s success with the Camp David Accords, Bill Clinton brought Palestinian leader Yasser Arafat and Israeli Prime Minister Ehud Barak to the camp for peace talks in 2000. Don’t expect any triumphant theater adaptations of this meeting, though — the two-week negotiations fell flat.

Arena Stage, 1101 Sixth St. SW; through May 4, various times, $55-$120; 202-488-3300. (Waterfront)