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Donald J. Trump likes to brag that he leads his Republican rivals in every poll, but a new poll on Monday showed him with company at the top of the field.

According to a survey of likely Republican Iowa caucusgoers from Monmouth University, Ben Carson is tied with Mr. Trump in Iowa. The poll marks the first time in more than a month that the billionaire tycoon was not leading a poll in one of the first four states to hold nominating contests.

Mr. Trump and Mr. Carson were deadlocked with the support of 23 percent of the Iowans who were polled. Carly Fiorina, Senator Ted Cruz of Texas and Gov. Scott Walker of Wisconsin made up the next tier of candidates.

The poll shows the growing appetite for political outsiders in Iowa and could spell trouble for more traditional candidates who were counting on the state to propel them to the nomination. Mr. Walker has seen his prospects in Iowa dampen substantially in recent weeks and candidates such as former Gov. Mike Huckabee of Arkansas and former Senator Rick Santorum of Pennsylvania, who were once favorites in the state, are barely registering with voters.

The Monmouth poll follows a survey from The Des Moines Register over the weekend that showed Mr. Trump leading in the state, but revealed that Mr. Carson is gaining ground.

Monday’s poll did show that Mr. Carson is leading Mr. Trump with people who consider themselves to be “very conservative,” with evangelical Christians, and with women.

“After more than a month of Trump winning virtually every Republican demographic group, we’ve finally got a little variation in voting blocs to talk about,” said Patrick Murray, director of the independent Monmouth University Polling Institute.

Monmouth’s poll of 405 Republicans had a margin of sampling error is plus or minus 5 percentage points.