Champ, who won his first PGA Tour title in his second start as a tour member at the Sanderson Farms Championship in MS last month, had eight birdies an eagle and one bogey on the El Camaleon Golf Club Course in Playa del Carmen.
Champ was sensational in just his third career PGA Tour start on Friday, mixing eight birdies and an eagle with one bogey for a round of nine-under par 62 that gave him the outright lead before Kuchar overtook him later in the day.
Cameron Davis and Matt Jones are the only Australians to have made the weekend at the Mayakoba Classic at Playa del Carmen near Cancun in Mexico but they are a long way from the lead of Matt Kuchar who produced consecutive rounds of 64 to lead by two over rookie Cameron Champ.
SHOT OF THE DAY: Full disclosure - we don't know exactly how this shot played out, but we're going with Champ hitting 3-wood over the cave bunker because it's so nice to look at.
Kuchar has gone more than four years since his last PGA Tour victory.
Champ said he never thought about the possibility of shooting a 59.
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Kuchar teed off on 10 and his three birdies in his first nine holes included an 18-footer at the 16th.
"It's kind of nice to look back and know that I've won on every stage", said Hickcok, who was also a two-time victor on the Mackenzie Tour a year ago.
Jordan Spieth missed the cut in his final event of the year. He had a 69 and was outside the cut line with half of the field still on the course in good scoring conditions.
Seven players are at 11 under, including defending champion Patton Kizzire, past Mayakoba champion Brian Gay and Anirban Lahiri of India, who's played in the last two Presidents Cups, and New Zealand's Danny Lee.
Rickie Fowler (68) and Tony Finau (65) were at 8-under 134, along with their Ryder Cup captain, Jim Furyk, who had a 65.
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