The poll found that 27 percent of Republican primary voters support Trump, while 21 percent said they favor Carson.
Trump’s six-point lead in the latest poll is slightly wider than the 27 percent to 23 percent lead he held over Carson in aCBS News/New York Times poll conducted last month.
Carson, a retired neurosurgeon, has seen a significant increase in support since coming in at just 6 percent in a poll conducted in August.
In the latest poll, Sen. Ted Cruz, R- Tex., comes in third at 9 percent, followed closely by Sen. Marco Rubio, R- Fla., at 8 percent.
Former Florida Gov. Jeb Bush and former Hewlett-Packard CEO Carly Fiorina are tied at 6 percent, while the other GOPcandidates have support in the low single digits.
CBS News noted Carson and Rubio are the most mentioned candidates when voters are asked who their second choice for the nomination would be.
On the Democratic side, the poll found that Hillary Clinton is holding on to a big lead over Sen. Bernie Sanders, I-Vt.
Forty-six percent of Democratic primary voters said they support Clinton, while 27 percent prefer Sanders. Clinton’s lead is nearly unchanged from last month.
The CBS News survey of 1,251 adults was conducted October 4th through 8th by SSRS and included 419 Republican primary voters and 343 Democratic primary voters.
The margin of error among Republican voters was plus or minus 5 percentage points, while the margin of error among Democratic voters was plus or minus 6 percentage points.