Kim is at 10-under 130 on the Old White TPC course. Tour rookie Scott Stallings shot 66 to move into second place at 9-under. Gary Woodland (67) and Webb Simpson (69) are two shots back.
Simpson was the second round co-leader with Brendon de Jonge. De Jonge shot 72 to fall five strokes behind.
Augusta native Charles Howell shot 70 and is six back. Blake Adams, of Swainsboro, Ga., also had 70 and trails by nine.
Kim's best round of the year left him with a chance to earn a spot in next week's Bridgestone Invitational with a win.
His last win came a year ago at the Shell Houston Open before he underwent thumb surgery and took three months off.