Carson, a retired neurosurgeon, received 26 percent of the support in the New York Times/CBS News poll released on Tuesday morning.
Trump placed second with 22 percent of the support of those surveyed, trailing by less than the 6 percentage-point margin of error. The poll of 575 Republican primary voters was conducted Oct. 21 through 25.
The Republican candidates will meet on the debate stage on Wednesday night, providing a third opportunity for them to differentiate themselves.
White House hopeful Carson under fire for Muslim comments
The national poll comes after three conducted in Iowa, the first state to vote in the primary process, showed Trump trailing Carson for the first time.
For months, Trump had appeared impermeable to attacks from his Republican rivals in the November 2016 race for the White House. Despite criticism, gaffes and attacks, the New York real estate mogul held a tight grip on the first-place position in dozens of polls.
There was one sign of encouragement for Trump in the poll. Of those supporting him, 55 percent said they had firmly made up their minds. Carson’s supporters were less certain, with 80 percent saying it was too early to say whether they would ultimately vote for him.
Republican candidate Carson says Muslims unfit to be US president
Carson and Trump held sizable leads over the rest of the Republican candidates. In a distant third place, Florida Senator Marco Rubio received 8 percent. Former Florida Governor Jeb Bush, who was once thought to be a likely front-runner, and former Hewlett-Packard Co Chief Executive Officer Carly Fiorina tied at 7 percent.
Four candidates - Kentucky Senator Rand Paul, Texas Senator Ted Cruz, Ohio Governor John Kasich and former Arkansas Governor Mike Huckabee - all tied at 4 percent.
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