Kuchar's bogey-free round is his best since February, according to Justin Ray of Golf Channel. He hit 15 of 18 greens in regulation while only missing two fairways at El Camaleon Golf Club.
Rickie Fowler carded the best round of the notable players in the field. He shot 66 on Thursday to sit in a tie for 19th.
The 2018 struggles continued for Jordan Spieth, who shot an even-par 71 in his debut round at the Mexican event.
Round 2 of the Mayakoba Golf Classic begins Friday at 7:00 a.m. ET.