Ted Cruz. Spencer Platt/Getty Images Ted Cruz may be gaining on Republican presidential frontrunner Donald Trump in the largest remaining state in the Republican primary.

A new USC Dornsife/Los Angeles Times poll of likely Republican voters published on Sunday showed the Texas senator, with 35% support, just 1 point behind Trump's 36% in California.

California is the largest and most delegate-heavy state remaining in the Republican nominating contest. In the poll, Ohio Gov. John Kasich, the third GOP candidate, logged a distant third with 14% support.

Other recent polls have mostly shown Trump with a large lead over Cruz and Kasich, and with the primary still over two months away, the polls could easily shift before election day.

Still, even if Trump wins the primary outright, Cruz's strength in California could still pose a problem for the real-estate magnate.

The Times/USC poll is one of the first released since Sen. Marco Rubio dropped out of the race, and could hint that Cruz has a shot at taking a large chunk of the delegates home in California. Thirteen delegates are awarded to the statewide winner, while the remaining ones are awarded by whichever candidate wins each district.

The Sunday poll also found Cruz's strength concentrated in Los Angeles County and the Central Valley, one of the more rural parts of the state. Some observers further speculated that Kasich could play well in Democratic-heavy coastal areas. Taken together, Cruz and Kasich's support in California could hinder Trump's goal of securing the 1,237 delegates needed to clinch the Republican nomination on the first round of voting.

California's primary is on June 7.