(Updates with Chambliss quotes)
By Roberta Rampton and Patricia Zengerle
WASHINGTON, May 6 (Reuters) - President Barack Obama took his second-term "schmooze offensive" to the golf course on Monday, bonding in a bipartisan foursome as Republican Senator Saxby Chambliss hit a hole-in-one.
Obama, an avid golfer with a respectable 17 handicap, rarely takes politics to the greens, preferring instead to golf with friends and staffers far out of the sight of the reporters who travel with him.
But he invited Chambliss and two other senators to play the south course at the Andrews military base in suburban Washington, part of his effort to advance his second-term agenda by having better relationships with Congress. .
Chambliss hit a five iron 156 yards for a surprise hole in one on the 11th hole. The feat was the talk of Washington, but the Georgia Republican was modest about the shot.
"It was pretty special. The ball actually flew the route I wanted it to go," Chambliss told reporters back at the Senate, after the game was cut short after 15 holes due to a vote.
"I'm the luckiest guy in the world to have a hole in one. Anyone who says having a hole-in-one is skill, they're living in another world," he said.
Obama paired up with Democrat Mark Udall of Colorado, the top-ranked golfer in Congress as measured by Golf Digest in 2011. The magazine estimated Udall's handicap at 2.
But the hole-in-one helped deliver the match to Chambliss and Bob Corker, the top Republican on the Senate Foreign Relations Committee, who has a 2.1 handicap.
"The president got it out of the hole and handed it to me, and then they brought the flag out later. He signed the flag, and everybody signed the flag, and it was pretty neat," said Chambliss, who has golfed for 40 years, and has a 7.4 handicap.
Obama has waged bitter fights with Congress over how best to tame the deficit and on proposed new gun control laws after December's school shooting in Newtown, Connecticut.
But the president has also been criticized for failing to work more closely with the Senate and House of Representatives. He has responded in recent months by hosting dinners and lunches with small groups of lawmakers from both parties to try to find common ground on issues.
Chambliss said the foursome did not discuss immigration reform, a top priority for Obama, which begins to wind its way through Congress this week.
Chambliss said the foursome talked "a little bit" about the crisis in Syria, cybersecurity and fiscal issues.
"Actually, I told him since I'd made a hole-in-one, he ought to give us everything we want on entitlement reform," Chambliss quipped.
But it was not a day for detailed policy debates.
"This was a day to get away from the office and the president seemed like he enjoyed himself and I know the three of us did, and it was just like playing with my usual Saturday morning foursome," Chambliss said.
"There was a lot of jawing back-and-forth on short putts," said Chambliss, who plans to frame the ball and flag. "It was just a fun day."
Obama golfed 113 times in his first term, according to Mark Knoller of CBS News, who keeps statistics on the president.
He played with House Republican Speaker John Boehner (handicap: 7.9) in June 2011 and has played twice with Democratic Representative Jim Clyburn (11.3) from South Carolina, in August 2009 and again a year later, Knoller said.
So far in his second term, he has golfed about a dozen times, including his first-ever round with Tiger Woods, the world's top-ranked golfer.
Golf handicaps are a measure of ability and a lower handicap signifies a better player. (Additional reporting by Steve Holland and Patricia Zengerle; Editing by Cynthia Osterman)