A young woman raised by her mother on an island in Greece is about to get married, and she wants her father to give her away. There’s just one problem: She doesn’t know who he is. When she learns that her father could be any one of three men who were with her mom on the weekend she was conceived, she invites all three to come to the island — signing the invitations with her mother’s name without revealing the actual purpose.

That’s the premise of Broadway mega-hit “Mamma Mia!” Diamond Head Theatre’s production — the first here by a Hawaii-based theater company — opens today, in a hotly anticipated show.

It’s a “jukebox musical” like no other. The songs were all written by Benny Andersson and Bjorn Ulvaeus — one-half of the Swedish mega-group ABBA — and they were all hits for the group. Playwright Catherine Johnson’s story isn’t about ABBA. Nonetheless, the songs give the show an instant hook with pop music fans of all ages.

“It’s going to be huge,” predicted John Rampage, Diamond Head Theatre’s artistic director. “I know people who have seen this show 10 or 11 times all over the world, wherever it was playing. They like the sense of total entertainment and the sense of fun that it brings.”

DHT worked for years to get the rights to do the show in Hawaii.

Two stage veterans, both Hawaii-born and with national credits, have been entrusted with the production.

Kimee Balmilero, a member of the original “Mamma Mia!” cast on Broadway, is the director. Mark Kanemura, known for his high-profile work on “So You Think You Can Dance” and with Lady Gaga, is the choreographer.

Balmilero said the opportunity to direct is “beyond what I would have ever wanted when I came home. I’ve been having so much fun.”

She’s been largely involved with presenting improv and sketch comedy onstage since returning to Hawaii four years ago — a move she described as “a scary moment” after years spent working or on the mainland.

“When we were putting together our team, we were looking for people who could not only sing and dance and act, but could also bring a little bit of themselves to the show,” she said. “The cast is really settling in, and it’s been wonderful to watch them.”

Balmilero got her start doing theater with Ron Bright. She auditioned for “Miss Saigon” in the fall of her senior year in high school and joined the national touring company when she graduated, spending the next 2-1/2 years on the road.

“I was never really a lead in high school, I was always happy being part of the ensemble,” she said. “But when ‘Miss Saigon’ ended, I didn’t want it to be my last thing. Right after we closed I went to San Francisco and I studied a little bit at Studio A.C.T. Then I went to New York.”

When she got there she went to every audition she could, “even if I knew I wasn’t technically correct for it,” she said, “because it was a opportunity for me practice my monologue. I didn’t have an agent. I had no representation, (but) I did have my Equity card, which was huge because it got me into auditions.”

A month or two in, the producers of “Mamma Mia!” held auditions, and Balmilero made the grade. Soon after that she was onstage on Broadway.

“That’s not a normal story for a lot of people, but I was working my butt off just to be seen,” she said. “The thing I was always comfortable with was being myself. When you’re going to these calls and you’re the 100th person that they’re seeing, the only thing that you have that nobody else has is you.”

Balmilero met ABBA’s Andersson and Ulvaeus on opening night. She described the experience as “really, really cool.”

After returning to the islands, Balmilero founded Improv HI, an improv and sketch comedy group, and the Hawaii Sketch Comedy Festival, which celebrated its second year at the Doris Duke Theatre in March. She also teaches improv and sketch comedy and is coordinator of the Extended Learning Program at Mid-Pacific Institute.

Kanemura said he is having a great time with the production. Directors are prohibited from changing the lyrics in a musical without permission from the lyricist or publisher. Choreo- graphers have more leeway — and Kanemura is taking full advantage of that.

“Kimee and I have known each other for about 20 years,” he said. “One of my first community theater productions was ‘Tommy’ at Manoa Valley Theatre (in 1996), and she was in that. From there we always clicked. … Because she was part of the original cast, there were some iconic movements that she wanted to keep, but for the most part she let me have at it.

“I love challenges, so it was very exciting for me to take it on and just jump right into it.”

The show brings Kanemura back to where his life in theater began as a member of the Show Kidz, the children’s theater program that preceded the Shooting Stars at DHT. He graduated to doing community theater in Honolulu, then worked at Tokyo Disney and danced and choreographed shows on cruise ships.

The big break that “propelled” Kanemura to Los Angeles and beyond was “So You Think You Can Dance” in 2008. Dancing with Lady Gaga came after that.

“It’s a full-circle moment,” Kanemura said. “It is such a cool moment for me to come back to the theater that kind of started it all for me.”