Sixteen-year-old Hull finished the day tied for third behind joint leaders Haeji Kang and So Yeon Ryu of South Korea.
World number one and defending champion Yani Tseng is part of a large group on even-par 72.
Hull had a better day than her caddie, whose motorbike was stolen from outside his hotel. He caught a taxi to the Royal Liverpool club in Hoylake, Merseyside.
"He made it in plenty of time. I didn't even know until he told me after the round," Hull said on the Ladies European Tour website (www.ladieseuropeantour.com).
Kang hit a double bogey and two bogeys but still finished the day with a share of the lead thanks to six birdies.
"I started with a bogey but I managed to stay calm out there," she said. "Especially in this kind of major, you have to be very patient.
"My iron shots were just inside 20 feet all the time, so I could just putt it out."