Not ones to waste an opportunity, Choi birdied the first five holes at Sherwood Country Club and Woods was nearly as good, with birdies on four of the five.
But then the winds reappeared with gusto and, while Woods struggled on the back nine, Choi held steady and the South Korean finished atop the first-round leaderboard with a six-under-par 66.
Woods, seeking his first win in two years, was tied for second place with Steve Stricker after both shot three-under 69s on the Jack Nicklaus-designed course nestled in the Santa Monica Mountains.
"Anything under par is a good day today, with the wind up," said Woods, a four-time winner of the 18-player tournament that benefits his charitable foundation and pays $1.2 million to this year's winner.
Choi agreed, saying through an interpreter that when the wind returned, "my mind-set was just to try and make par and try to be patient." Which he did, making only one bogey in the round, on the par-three 15th.
It didn't hurt that Choi now lives in Dallas, "where there's 20-, 30-mile-an-hour winds every other day," he said. "I'm used to practicing in those conditions."
This was the third appearance in Woods' event for the 41-year-old Choi, who won the Players Championship in May and won $4.4 million on the PGA Tour this year. Choi's previous best finish at Sherwood was sixth in 2003.
A key shift in the round came when Choi birdied the par-five 13th hole to reach six under par while Woods was running into trouble.
Playing the 186-yard 15th hole, Woods' tee shot flew over the green and came to rest on a steep hill. Standing with a tough downhill lie, Woods' chip stopped short of the green, forcing him to chip again. He made a bogey four and dropped to three under par.
Then Woods took four shots to reach the green on the par-five 16th for a second consecutive bogey. But he rebounded with a birdie on the 17th, another par three.
Woods said the problem with the swirling wind was "you didn't know which way it's coming from. Then you have intensity changes on top of that. It's really hard out there."
Even so, when Woods was asked whether he was satisfied with being three shots behind the leader with three rounds remaining, he replied, "Absolutely." Woods and Choi were scheduled to be paired together Friday.
Stricker, fighting a cold, tied Woods by sinking a 40-foot birdie putt on the 18th hole. He also said Woods, who has been grappling with knee and tendon injuries and a new swing during the last year, is regaining his form.
"He's striking the ball so solidly," Stricker said of Woods. "He's putting better and hitting it better, driving it better. It looks like the Tiger of old, really, and it's great to see."
Several others struggled Thursday, including rookie Keegan Bradley, who won the PGA Championship and was making his first appearance in Woods' tournament. Bradley shot a five-over 76. Martin Laird had a 77 and Paul Casey a 79.