Carson, a retired neurosurgeon, received 26 percent of the support in the latest New York Times/CBS News poll, AFP reported on Wednesday.
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 Wednesday night, providing a third opportunity for them to differentiate themselves.
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. 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.
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.
Ex-Florida Governor Jeb Bush, who was thought to be a likely front runner, and former Hewlett-Packard CEO Carly Fiorina tied at 7 percent. Four candidates – Kentucky Senator Rand Paul, Texas Senator Ted Cruz, Ohio Governor John Kasich and ex-Arkansas Governor Mike Huckabee – all tied at 4 percent.