In the second poll taken since the Kentucky primaries and the first since Republican Rand Paul talked openly about his reservations with certain aspects of the 1964 Civil Rights Act, Paul leads Democrat Jack Conway by 3 points, according to the DailyKos/Research2000 survey (May 24-26, 600 LV, MoE +/- 4%).
People should be dubious of this poll for a number of reasons. First, it's commissioned by the Daily Kos. That's not exactly a bastion of objective polling. Second, here are the internals. 80% of Republicans were voting for Paul. 76% of Democrats were voting for Conway and Paul beat Conway by 43-31 among independents. Now, Kentucky is Republican heavy state. So, getting more of his own party and winning solidly among independents, we're supposed to believe that Paul is only up by 3%. That's misleading but it does appear as though the race has tightened.