When 28-year-old Alexandria Ocasio-Cortez came from nowhere to defeat Rep. Joe Crowley in the Democratic primary for New York’s 14th Congressional District, she became a media darling overnight. Time magazine called her win “the biggest upset of the 2018 elections so far.” Within days Ms. Ocasio-Cortez was appearing on “The Late Show with Stephen Colbert” and “The View.”

Now Republicans looking for their own Ocasio-Cortez think they may have found her. Meet Elizabeth Heng—a Republican running in California’s 16th Congressional District. Like Ms. Ocasio-Cortez, Ms. Heng is young (33). Like Ms. Ocasio-Cortez, she’s a racial minority (Cambodian). And like Ms. Ocasio-Cortez, she’s a millennial female running against an established male politician.

What makes her race interesting is California’s “jungle” primary system, in which candidates of all parties run against one another. The top two finishers then face off in November’s general election. California’s 16th is a reliably blue district in a state practically synonymous with the term “blue.” But a funny thing happened on the way to this year’s primary: The virtually unknown Republican woman came within 6% of beating incumbent Democrat Jim Costa in a head-to-head matchup.

In the June primary Ms. Heng received 35,080 votes to Mr. Costa’s 39,527. To put this in perspective, Ms. Ocasio-Cortez received 16,898 votes to Mr. Crowley’s 12,880. And again, Ms. Ocasio-Cortez had an easier task, trying to prove she’s the best Democrat in a Democratic district. By contrast, Ms. Heng must persuade Democratic voters to give a Republican a chance.

Keep reading William McGurn's column in the Wall Street Journal.