Kuchar, who had been winless for almost four years until his win at the Mayakoba Classic late in 2018 now appears likely to add a 9th PGA Tour title just three months after his 8th.
Shugo Imahira is six shots off the pace after carding a 3-under 67. That put him at No. 4 in the world, the highest he has been in his career.
Second-placed Putnam birdied his final hole, the par-five ninth, thanks to a deft 30-yard pitch over a bunker and down to inside three feet. Reavie had five birdies through nine holes but after he made the turn, his scorecard was colored with three consecutive bogeys.
Keith Mitchell surged into joint third place after making seven birdies in a round of seven-under 63, and joined Chez Reavie on 14 under overall.
Matt Kuchar continued his serene progress at the Sony Open in Hawaii as he claimed a two-shot lead after the third round.
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He recorded an 18-under 192 total, while Putnam drained a birdie at the last for a 67 to go 16-under. He opened the round with birdies on each of the first three holes. There are a lot of good players out there. "Still got a chance".
Bryson DeChambeau tied his career low round of 63. He didn't make any, but he didn't leave himself any work for par.
Mitchell played a bogey-free round of 63, including four straight birdies on Nos.
"Apparently, I need to go buy a lottery ticket today", Reavie said.
He became eligible for the winners-only field at Kapalua last week by winning at another beach resort - Mayakoba - last year, opening with rounds of 64-64, the kind of start he has enjoyed at Waialae.
DIVOTS: Gary Woodland, who didn't shoot worse than 68 last week and still had to settle for runner-up at Kapalua, was among 10 players who missed the 54-hole cut because more than 78 players made it to the weekend.