Actually, Foreign Service rankings only reach the equivalent of four-stars -- and that's for career diplomats. When asked to clarify, Kounalakis said she misspoke, but emphasized she was the highest U.S. official in Hungary.

Kounalakis is well connected politically. Her father, Angelo Tsakopoulos, is a prominent real estate developer in Sacramento. He’s contributed millions of dollars to causes and candidates, mostly Democrats, at the local, state and national level, including more than $120,000 to support Hillary Clinton’s 2016 campaign.

Kounalakis herself gave more than $170,000 to Clinton for her most recent presidential bid. But she brushes off claims she’s just another wealthy person trying to make a splash in California politics.

"I think that people are really pushing back on the idea that they are going to stand by and allow qualified, viable women candidates to be discounted and minimized and just waved away," she said.

Kounalakis, who's been endorsed by Sen. Kamala Harris, said people have encouraged her to run her for years, and that they’re backing her campaign with contributions. Last year she raised about $2.5 million, although a third of that was her own money.

“It is the hardest thing for women candidates to do, to raise money, and I’ve raised the most," she said.

Lt. Governor candidate Eleni Kounalakis speaks to the crowd at the California Democratic Convention. (Kounalakis Campaign)

Maimuna Syed is executive director with Emerge California, which trains Democratic women to run for office. She said the inability to raise money has tripped up many women candidates. But she said this year -- following the election of Donald Trump and the rise of the Me Too Movement -- women are getting more support.

“I think, what we’re seeing, this is more of a willingness for institutional organizations and also for everyday people to say, look, we need more women in office and I’m going to help support them and I’m going to help fundraise for them," she said.

But money isn’t the only factor in the race, there’s also a strong field of competitors, including State Sen. Ed Hernandez. He’s racked up congressional and legislative endorsements and his campaign said he has a strong record of supporting women's issues. Attorney Jeff Bleich served as a senior adviser to President Obama and was his ambassador to Australia.

With three strong candidates running, none got the party’s endorsement at the recent state Democratic convention.

Congresswoman Jackie Speier, who ran for lieutenant governor in 2006, said whoever is elected in November will face another challenge.

“The problem with the lieutenant governor's position is that, unless you have a governor working with you, you’re limited in what you get to do," she said. "You have to have a governor who is going to be supportive of you to give you the opportunity.”

That’s a challenge Kounalakis would surely welcome. But win or lose, she said it’s important for women simply to be in the game.

Ed HernandezEd Hernandez

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