(CNN) -

In one of the most closely-watched Senate races of the year, incumbent Democratic Sen. Kay Hagan of North Carolina holds a narrow three-point advantage over her Republican challenger, according to a new CNN/ORC International survey.

But the poll indicates that Thom Tillis, the GOP nominee, may be falling behind Hagan because a Libertarian candidate could be siphoning off Republican votes.

Hagan edges Tillis, 46%-43%, while Libertarian Sean Haugh has support from 7% likely voters, according to the poll.

The three-point gap between Tillis and Hagan, however, is well within the poll's sampling error of plus or minus four percentage points among likely voters, meaning the candidates are about even.

The race is one of eight Senate contests that CNN rates as "up for grabs" this fall. As Republicans seek to retake the Senate majority, they consider North Carolina one of their best chances to pick up a Democratic seat.

Since Hagan was first elected in 2008, North Carolina has transitioned from somewhat of a purple state to solid red territory. Republicans took the governorship and seized both houses in the state Legislature, and North Carolina was one of two states that voted for Barack Obama in 2008 but Mitt Romney in 2012.

Hagan's favorable rating is 46 percent, indicating that everyone who likes her is going to vote for her. But Tillis gets a 47 percent favorable rating among likely voters, yet only 43 percent of the vote.

"That suggests that there are voters who would probably choose Tillis in a two-way race but aren't going to vote for him in a three-way contest," said CNN Polling Director Keating Holland.

While Haugh only has the backing of 7 percent of voters, his presence in the race could be hugely influential if Tillis ends up losing to Hagan by just a few percentage points.

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Poll: Libertarian could spoil N.C. race