UPDATED 11/3/10 – 6:18 p.m.

CHICAGO (WBBM) — After months of nasty fighting, U.S. Senator-elect Mark Kirk and his Democratic rival Alexi Giannoulias buried the hatchet by sitting down to have a beer together Wednesday night.

A day after Kirk won the election for President Barack Obama’s former Senate seat, Kirk and Giannoulias sat down for a beer at about 6:15 p.m. Wednesday at the Billy Goat Tavern on Lower Michigan Avenue. Kirk showed up dressed in a dress shirt, blazer and khaki pants; Giannoulias was dressed far more casually in jeans, a sweatshirt and a Chicago Blackhawks cap.

Kirk, a Republican congressman from Northbrook, extended the invitation for a beer to Giannoulias during his victory speech late Tuesday.

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“Alexi and I, during this campaign, we discussed having a beer when this is all over,” Kirk said. “The first round is on me.”

Billy Goat owner Sam Sianis told CBS 2’s Dana Kozlov that he has one rule for the candidates: no fighting.

“Out the door. Inside the door, you come into here … to have fun,” Sianis said. “No fighting, no fighting. Is fun only. … The politics, leave them outside now. Out the door. The politics, when you’re here, you no talk about the politics, you talk about the good times, how good the beer is … the cheezborger, and all that.”

On Wednesday, Kirk said the get-together with Giannoulias would show that “once the voters have spoken,” candidates can let bygones be bygones and work together for the good of the country.

The senator-elect actually won two races on Tuesday. The first was to fill the vacancy left when President Obama left the Senate. Roland Burris was appointed to fill that spot, but a federal court ruled that a special election must be held to fill the rest of that term.

The second race was for a full six-year term starting next year.

Kirk said he hopes to be sworn in as quickly as possible, maybe in the next couple of weeks, during the lame duck session of Congress.

Kirk promised to be a “very independent” senator who is a “fiscal conservative, social moderate and national security hawk.” He also said he “absolutely” would work with President Obama.