Kentucky Senate candidate Rand Paul (R) is leading his Democratic challenger, Jack Conway (D), in a poll released Thursday.

Paul, who recently found himself in hot water for questioning the legality of portions of the Civil Rights Act, is leading Conway 44-40 percent with 9 percent undecided in a Daily Kos/Research 2000 poll taken May 24-26.

The margin of error is 4 percent, so Paul, an eye doctor, is statistically tied with the state attorney general. The survey polled likely voters.

Paul maintains a 53-33 favorability/unfavorability rating, showing that his comments about the Civil Rights Act have not caused major losses in support.

"This race's big battleground will be independent voters — Paul is currently winning them 42-31, with 27 percent undecided, and Democrats, where Conway is only getting 75 percent to Paul's 7 Percent, with 18 percent undecided," the site's founder Markos Moulitsas writes.