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The border was mapped incorrectly in 1818, when surveyors mistakenly set the line about a half-mile south of the 35th parallel, according to Georgia legislators.
A similar proposal passed the Georgia General Assembly last year, but nothing came of it.
Some senators suggested that Georgia should go to court over the border, but others said the state should take a gentler approach.
"When one has a disturbance with a neighbor, it's always best to walk to the fence line and have a discussion before calling the law," said state Sen. Jeff Mullis, a Republican from Chickamauga who voted against the resolution. "We should resolve it in a peaceful manner ... instead of siccing a bunch of lawyers on our neighbors north of us."
House Resolution 51 calls for three representatives and three senators to be appointed to a boundary line commission that would contact elected officials in Tennessee and North Carolina. If those states don't negotiate, the border commission could recommend other steps to reclaim the land.