Illinois state Treasurer Alexi Giannoulias (D) leads Rep. Mark Kirk (R-Ill.) by three points, 46-43, in an internal poll in their Senate race.

The Greenberg Quinlan Rosner Research poll also shows former Chicago Inspector General David Hoffman (D) trailing Kirk 48-39.

Kirk and Giannoulias have polled close to each other in the general election, but surveys have been sparse to this point.

Giannoulias’s poll shows him with a favorability rating of more than two-to-one.

The release of the poll appears to be aimed at showing he is a better general election candidate than Hoffman. At this point, Giannoulias likely has much higher name recognition than the insurgent challenger, who raised and self-funded a combined $888,000 in the third quarter.

The pollster points out that Giannoulias is even performing better than Hoffman in the Chicago media market.

It does not provide numbers on their Democratic primary matchup.