Thompson, a graduate of the developmental Korn Ferry Tour, was seven-under through six holes thanks to his eagles at the fifth and sixth on the La Quinta Country Club course, one of three in use for the event in the Southern California desert along with the Nicklaus Tournament course and the Stadium course.
His 10-under par total of 62 put him two clear of five players, a group led by fourth-ranked Spaniard Jon Rahm and including Americans Tyler Duncan, Taylor Montgomery and Sam Burns and German Matti Schmid.
Thompson already had three birdies under his belt when he eagled the par-five fifth.
He missed the green at the par-five sixth but chipped in for another eagle, becoming the first player to eagle consecutive holes in a PGA Tour-sanctioned event since Shane Lowry in the third round of last year's Open Championship.
He added a birdie at the ninth to make the turn at eight-under.
The former top-ranked amateur said staying focused on each shot was his main task coming in.
"That was kind of like my biggest challenge today was staying present-minded and trying to put one foot in front of the other," said Thompson, whose two birdies on the back nine included an exclamation point at the 18th.
"Your mind definitely starts to wander a little bit. But I played enough rounds to where I try to teach myself over and over you can't get ahead of yourself."
Thompson, who has made 19 starts on the PGA Tour as an amateur and a pro, said he still feels like a rookie - especially at a tournament that features three new courses to learn.
"You kind of have to play practice rounds pretty fast and kind of figure out what you want to do during the week," he said.
"But at the same time it kind of goes both ways. You don't put as much stress on yourself kind of preparing for every course because you're trying to see every hole."
Rahm, who also opened his week on the La Quinta course, is no stranger to the event, which he won in 2018.
His nine birdies included three in a row at the fifth, sixth and seventh and another three straight at the 11th, 12th and 13th.
Solid Rahm
"It's a great start to the tournament," said Rahm, who won the Tournament of Champions in Hawaii two weeks ago.
"Solid round of golf, great putting out there. Hopefully I can keep that going the whole week and feel a little bit better tee to green."
Rahm said he was happy to get his round at La Quinta, usually the easiest course in the rotation, done before the winds are expected to pick up on Friday.
"It can show some teeth because some of those fairways are quite narrow to hit," he said.
Rahm is among five of the world's top 10 players in the field this week.
Second-ranked Masters champion Scottie Scheffler, who again has a chance to supplant Rory McIlroy at number one this week, opened with a four-under par 68 on the La Quinta Country Club course.
So did world number five Patrick Cantlay - who also has a slim chance of reaching number one this week.
World number six Xander Schauffele headlined a group of nine players sharing seventh place on 65, while seventh-ranked Will Zalatoris carded a three-under par 69.
