The elite 18-player field had to contend with the gusts that rushed through the canyons in which the Sherwood Country Club is located.
Choi shot a 6-under 66 while Woods and Steve Stricker were tied for second at 3-under 69.
The winds did not begin to blow until the first groups reached the turn, but then the course became a major challenge. Woods played the first five holes in 4-under and was then 1-over the rest of the way.
"It didn't start blowing till we were on sixth green, but then it was dancing all over the place," Woods said. "It was tough. It's hard to hit the ball pin-high."
Kuchar was 4-under for his round until he made a triple-bogey at the par-5 16th.