That left the Venezuelan among a pack of 11 golfers one stroke back of American co-leaders Hudson Swafford, Matt Every, Brandon Hagy, Kevin Chappell and Ollie Schniederjans.
Level with Vegas were K.J. Choi, 2004 winner Vijay Singh and twice U.S. Masters winner Bubba Watson, who enjoyed his first bogey-free round of the season.
Another 15 golfers had yet to finish their round, including American Kramer Hickok, who was five-under through 17 holes, and 19-year-old Australian Ryan Ruffels, four-under through 16.
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World number one Dustin Johnson was making his own charge with four front-nine birdies but failed to find any consistency after a two-hour rain delay that began right after his tee shot at the 10th landed next to a parking lot.
Johnson, who said this week that he is still feeling the effect of the freak back injury he suffered in April, ended up with a five-under 67, only two strokes off the pace in a huge group tied for 17th.
Britain's Ian Poulter and Canadian Mackenzie Hughes, who is looking to become the first homegrown champion since Pat Fletcher in 1954, were also two behind the leaders.
Kuchar felt dizzy a couple of times during his round, including once when he was marking a ball, and even met with an on-course medic.
"I had a couple of spells where I got a little bit dizzy and I felt weak. I don't know where it came from," said Kuchar, who did not blame jet lag after flying to Canada from England where he narrowly missed out on a maiden major title.
"I've had plenty of time to get over the travel. Hopefully it's just something that passes real quick."
(Reporting by Frank Pingue in Toronto; Editing by Ian Ransom)
