Choi birdied the par-five 18th to shoot even-par 72 and join Brown (70) at nine-under-207, one shot ahead of Jimmy Walker and Gary Woodland at Torrey Pines in southern California.
Twenty-three players are bunched within four shots on a packed leaderboard, with rain and strong winds forecast to lash the course in the final round on Sunday.
Choi, winless on the PGA Tour since 2011, was delighted to give himself a chance of ending his drought.
"This course is very important on the tee shot and second shot but more important is iron play," the 45-year-old told reporters.
"Today my greens in regulation was a little bit low, but my chipping was good and the putting was good."
Co-leader Brown recently became a father for the second time, but on Sunday will be focussed on trying to secure his second tour victory.
“Any time you're close to the lead or in the lead, it's obviously pretty good feeling,” he said.
“I've been driving it well for three days, really, and hopefully if I can continue that tomorrow, I'll be able to post another decent number. The weather's going to be brutal, so we'll just see how it goes.”
Swede Jonas Blixt shot his second straight 66 to vault within two shots of the lead, an unlikely position after he opened with a 77.
Nobody has recovered from such a poor start to win the tournament.
Fuzzy Zoeller overcame an opening 76 in 1979 and Pete Brown did the same in 1970.
“You don't get too many chances to win on this tour, and when you do, you really got to try to get it,” said Blixt, the 2014 Masters runner-up with Jordan Spieth.
“I felt like there was a low score out there on the South Course. I shot low here before and figured maybe I can have one of those rounds today and hopefully one tomorrow. We'll see what happens.”
The day provided plenty of excitement, with American Ben Crane and Swede Freddie Jacobson both holing out with long irons to eagle the par-four 15th, but Jason Gore’s albatross from 250 yards an the par-five 18th was the pick of the bunch.
(Editing by Andrew Both)
