(CNN) - A new poll indicates that the battle for Kentucky's open Senate seat is dead even.
According to a new CNN/Time/Opinion Research Corporation survey of registered voters in Kentucky, 46 percent support Republican nominee Rand Paul, with an equal amount saying they back Democratic nominee Jack Conway. Five percent of those questioned say they'd vote for neither candidate if the general election were held today, and four percent have no opinion.
"Not surprisingly, Paul is winning among conservatives by more than 40 points," says CNN Polling Director Keating Holland. "But Conway has a 22-point advantage among moderates."
Paul holds an 11 point advantage among independent voters, according to the survey.
Paul, an eye surgeon and the son of former GOP presidential hopeful and Texas Rep. Ron Paul, defeated Kentucky Sec. of State Trey Grayson in a divisive primary. Paul enjoyed the support of many in Tea Party movement, while Grayson was backed by many establishment Republicans.
Conway, Kentucky's attorney general, topped Lt. Governor Don Mongiardo in a bitter primary contest.
The winner will succeed Republican Sen. Jim Bunning, who is retiring at the end of the year.
Kentucky is considered a red state. Sen. John McCain topped then Sen. Barack Obama by 16 points in the state in the 2008 presidential election and George W. Bush took Kentucky by 20 points in his 2004 re-election.
"The area around Lexington and Frankfort in the central part of the state looks like it will be the real battleground in Kentucky this year," Holland adds. "The two candidates are essentially tied there - 47 percent for Paul and 45 percent for Conway."
The CNN/Time/Opinion Research Corporation poll was conducted September 2-7, with 869 registered voters in Kentucky questioned by telephone. The survey's overall sampling error is plus or minus 3.5 percentage points.
CNN Deputy Political Director Paul Steinhauser contributed to this report