Choi recorded six birdies against one bogey over the first 14 holes on Saturday before consecutive double-bogeys on Nos.15 and 16 dropped him to one under.
He recovered to birdie the final hole, leaving him one shot ahead of Australia's Richard Green entering the final round at Carnoustie Golf Links.
Choi, 54, is seeking his second win on the Champions Tour. The South Korea native tied for 14th at the event last year and has four top-10 finishes in 2024.
He said he was happy with his performance on Saturday despite the two late-round hiccups and is eager for the chance to secure his first major title.
"It's a dream come true," Choi said. "The Open is (a) very special event."
Choi said he will focus on better control with his iron shots and his putts as he shoots for his first Champions Tour win since the 2021 PURE Insurance Championship.
Green shot a 68 on Saturday, stacking six birdies against a pair of bogeys. He sat at one under after bogeying the 11th before tallying three more birdies to finish the round four under.
Like Choi, the 53-year-old Green has yet to win a Champions Tour major. Green has a third-place finish and a second-place finish this year.
"You've got to learn in those situations to deal with the pressure the right way," Green said of his two close calls earlier this year.
"As much experience as you can have in those situations is good. I'm going to take that little bit of experience out of those events and see how I go."
India's Arjun Atwal moved into third place at six under after carding the lowest round for the second straight day.
Atwal shot a five-under 67 to move two strokes within Choi for what would be the 51-year-old's first Champions Tour title.
"I didn't hit it all that great today, but I got some lucky breaks in the rough to where I had some good angles into the greens and I took advantage of that," said Atwal.Â
"I putted really well. I just wanted to give myself a chance for tomorrow. So I think I've done that."
Ireland's Padraig Harrington, who has finished second at the event in each of the last two years, is tied sixth with Canada's Stephen Ames at two under. Ames entered Saturday two shots behind Choi for the lead before shooting a two-over 74.
Australian Greg Chalmers (70) moved up eight places to tied 13th and is one over for the tournament.
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