Matteson led by a shot after 36 holes.
Steve Stricker, who also shot 66, sits in second place at 15-under in his quest for a fourth consecutive tournament title here.
Stricker birdied four holes in a row beginning at the 14th, but bogeyed the par-4 18th, stubbing a chip shot and missing a 15-footer for par.
Both Matteson, a former Georgia Tech standout, and Stricker bogeyed the last hole, setting up their final-round pairing together at TPC Deere Run, where Stricker is a fan favorite.
Former Masters Tournament champion Zach Johnson also carded 66 to climb into contention at 14-under, along with left-hander Brian Harman, a former Georgia golfer.
Billy Hurley, J.J. Henry and 2006 champion John Senden are tied for fifth, five strokes behind. Hurley’s 64 matched the best round of the day, while Senden eagled the par-5 second hole en route to a bogey-free 67.
“It’s great for me if I win,” said Matteson. “If Stricker wins, it’s a really big story.”
Stricker is attempting to join Tom Morris Jr., Walter Hagen, Gene Sarazen and Tiger Woods as a winner four consecutive times in the same tournament.
Woods has accomplished the feat twice.
“I can’t even believe three years have gone by,” said Stricker, who was five strokes behind Matteson at one point during the back nine.
Despite a bogey on the 18th hole, Stricker posted his 37th under-par round at Deere Run in 39 attempts, and is 109-under at the course since the tournament moved here in 2000.
Johnson, whose gallery in the third round rivaled Stricker’s, is from nearby Cedar Rapids, Iowa, and is a member of the tournament’s board of directors. While chasing his first win at Deere Run, he understands Stricker could make history.
“If I can’t win it, I wouldn’t mind seeing him win it,” Johnson said. “It’s not hard to be a fan of his. But anything can happen. There are guys behind making birdies.”
Deere Run, one of the easiest courses on the PGA Tour, is a haven for birdies and eagles, and Matteson also took advantage.
“Making two birdies early got me relaxed,” Matteson said. “But the bogey on 18, that was just a mismatched putt I hit downhill too hard.”
In contrast to Stricker and Johnson, Matteson played in relative seclusion, even though he was in the final pairing with Harman. There was little applause when his approach shot landed on the 18th green.
“Nobody’s paying attention to what I do,” Matteson said. “I just kind of play. I’m in a different position in life (than Stricker and Johnson). These guys are winning major championships. People buy tickets to see them.
“You have to put in the years to get on the other side of the fence.”