Kuchar, who prevailed in a playoff at this year's Henrico County Open, posted a 3-under 68 and is alone in second place at 11-under-par 205.
Aron Price matched the lowest round of the tournament on Saturday with a 7-under 65. He is tied for third place with Matt Weibring, who carded a third-round, four-under 68, at minus-10.
Snedeker, who won this year's Scholarship America Showdown and lost in a playoff at the Chattanooga Classic, appeared to be in good shape as he brought a three-stroke lead into round three.
He wasted little time in breaking into red figures with a birdie at the first and a birdie at the par-5 fourth. He added another birdie at seven, but dropped a shot a nine, his first bogey since his fourth hole in Friday's second round.
Snedeker reclaimed the lost stroke with a birdie at the 10th, but trouble loomed for the 25-year-old positioned 16th on this year's Nationwide Tour money list.
Snedeker owned a four-shot lead, but back-to-back bogeys at 13 and 14 tightened up the contest. Kuchar, a former winner on the PGA TOUR, was even through nine holes, but three back-nine birdies, including one at 17, got Kuchar within one.
Snedeker birdied the 17th hole to extend his lead to two. He parred his final hole and will be in position to secure his PGA TOUR card for next year as he will surely finish inside the requisite top 20 on the money list.
'All in all, it was a good day,' said Snedeker. 'I didn't drive it as well today and I paid the consequences for it. But I still putted pretty well and other than a couple of missed clubs, I played well.
'I was trying to run away and hide. But two bogeys back-to-back brought me back to reality. Hopefully, I'll hit a few more fairways and make it easy on myself tomorrow.'
Andrew Buckle and Craig Bowden both shot rounds of 4-under 68 and are tied for fifth place at 9-under-par 207.
John Merrick, who shared second place after the second round, only managed an even-par 72 on Saturday. He is knotted in seventh place with Chris Parra, who posted a two-under 70 in the third round, at minus-8.
Matthew Jones (68) and Dan Buchner (73) share ninth place at 7-under-par 209.