Andrew Putnam kept himself in contention with a three-under 67 and sits two shots adrift of Kuchar in second place.
"To shoot 7 under back-to-back is unexpected, but awfully excited", Kuchar said with the same smile he wears for most any occasion.
Veteran Kuchar has a career-best 54-hole score in Hawaii as the American tries to win for the ninth time on the US PGA Tour. He also had a 126 in Las Vegas in 2008.
Former major championship winners Jordan Spieth and Zach Johnson missed the cut by one stroke on Friday.
"Apparently, I need to go buy a lottery ticket today", Reavie said.
The Australian shot a two-under 68 third round to get to 11-under at Waialae Country Club in Honolulu on Saturday.
The PGA Tour began keeping hole-by-hole records in 1983 and no one had made three eagles in one round on par fours since. The Saitama native fell three places down the leaderboard following his opening round of 65.
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"I've got grey hair", he said with a laugh. "I want to do my best to aim for a top-10 finish". Those were the only players within five shots of the lead, and all of them are chasing Kuchar. He closed with a birdie Saturday to cut Kuchar's lead to just two.
No one had a more memorable round than Reavie.
He added his next eagle from 150 yards at the 16th and, as if that was not enough, made another from 135 yards at the sixth hole. He holed out from the fairway three times for eagle, all on par fours, to create golfing history. Reavie didn't think all that much about it until he piped a drive on No. 8 and hit a wedge that covered the flag.
"Before the other two I just hit the shot and I was trying to see if it was going at the hole. You're always surprised when they drop".
Cink made nine birdies in his round of 62. (68) and Marc Leishman (68) are also in the bunch at 11-under. Teryn Schaefer presents the best social media posts from around the world of golf in "Good, Bad & Unusual" and after each day's play brings you the biggest talking points in "The Takeaway". He has been to five of the islands, and plans to stay another few weeks after the Sony Open. Check in for highlights from every tournament plus player interviews, player profiles, tournament previews, swing analysis and all the greatest shots and incredible moments.
Kuchar had been suffering from a PGA Tour win drought of more than four-and-a-half years until he broke through in November at the Mayakoba Golf Classic for win No. 8.
The 40-year-old Kuchar was 3-under on the front side and regained the solo top spot.
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