Lin, who led Thursday after an opening 65, made three birdies against a lone bogey to join Hull on 11-under 202 through 54 holes at Old American Golf Club at The Colony, Texas.
New Zealand's Lydia Ko and France's Celine Boutier shared third on 203 with Canada's Maddie Szeryk fifth on 204.
Thailand's Moriya Jutanugarn and Atthaya Thitikul and South Korea's Ryu So-yeon were together on 205.
Lin, from Guangzhou, is chasing her first LPGA title. Her best finish was a runner-up effort in March at Thailand after losing a playoff to Dane Nanna Koerstz Madsen.
"Definitely have a chance," Lin said. "Just need to be patient.
"It's exciting and nervous at the same time, but I've experienced it a couple time this year, so I think I'm getting more comfortable about it. It's just still just playing your own game. Doesn't really matter who you're playing with."
Hull, meanwhile, seeks her second LPGA triumph after capturing the 2016 Tour Championship.
Hull, two strokes ahead of Lin when the day began, sandwiched birdies at the fourth and par-5 sixth holes around a bogey at the par-3 fifth, but fell from the lead with a double bogey at the 10th.
"I just hung in there and got around level par, so it wasn't too bad," Hull said. "I was swinging it quite well, so I'm not going to let one bad swing affect me.
"It wasn't really that bad. Hit the cart path and rolled into the rough, and then it was a bit of a dodgy drop because it was just awkward. Finished on level so it was all right."
Lin, who had grabbed the lead with birdies at the fifth, sixth and 12th holes, saw her lead trimmed when Hull birdied the 15th and Lin took her lone bogey at the par-3 16th to slide into a share of the lead with Hull.
"Overall, shooting under par, I'm pretty happy with it," Lin said. "But the only thing is I finished the round a little weaker. I make a bogey on 16 and didn't manage to get birdie on 17 and 18. Tomorrow hopefully I'll do better than that."
Boutier made her sixth birdie of the day at 18 to close out a 66 and finish one off the pace.
Ko overcame a double bogey at the par-3 11th with birdies on four of the next six holes to lift herself into contention.
