Political scientists say that if a lot of Republican voters stay home, conservative Steve Lonegan could have a chance to upset front-runner Chris Christie. Assemblyman Rick Merkt is also in the race.
The winner will face Gov. Jon Corzine in the general election in November. The Democrat also has primary competition, but no one has mounted a substantial campaign against him.
It's been 20 years since even one-fifth of the state's voters participated in a gubernatorial primary.
State Assembly seats and local offices are also on the ballot across New Jersey.
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