Rosie Jones is alone in third place after a 5-under 67 at Royal Evian Golf Club, followed by Janice Moodie and Jeong Jang, who share fourth place at 4-under-par 68.
Annika Sorenstam is back on tour after pulling out of the Canadian Women's Open two weeks ago. She opened her title defense this week with an even-par 72 and is part of a group tied for 31st.
At the par-5 seventh, Ochoa reached the putting surface in two with a 3-wood and drained the 20-footer for eagle. Two holes later, at the next par-5, Ochoa once again reached in two but this time two-putted for birdie from 30 feet.
A birdie at No. 9 polished off a front-nine 29, which matched Susie Redman's nine-hole tournament record from 2000.
'I've shot 29 before,' said Ochoa, a tour rookie who dominated collegiate golf at the University of Arizona. 'It was pretty incredible, especially my eagle putt on No. 7. That was a really good feeling.'
Ochoa did not have the same fortune on the second nine. She missed a pair of eight-footers for par at 12 and 13 but came back to tie Inkster for first with a 10-foot birdie putt at No. 16.
'I knew the back nine is a lot tougher than the front nine, so I knew that I wasn't going to be able to shoot another 29,' said Ochoa. 'You're going to make mistakes once in a while. I was very happy with how I finished.'
Ochoa has been nothing short of spectacular in her rookie campaign, including five top-6 finishes. In college, she collected 12 wins, including eight in a 10-tournament span.
'When I played in college, I played very well and learned very much,' said Ochoa. 'I thought I could get here and be good, so I'm just trying to do the same thing I did when I was in college.'
Inkster, whose amateur career was highlighted by three U.S. Women's Amateur titles in a row from 1980-82, did not have the kind of start as her younger co-leader.
She only managed three birdies on the front side but holed an eight-footer for birdie at No. 10 to reach 4-under par for the championship. Inkster, a member of the LPGA Hall of Fame with seven major titles to her record, knocked a 5-iron to 18 feet to set up birdie at the par-3 14th, but trouble loomed.
At the par-5 15th, Inkster drove out of bounds and was forced to head back to re-tee. By the time she reached the green, she had a five-footer for bogey but the putt never touched the hole and Inkster walked off with a double-bogey.
Inkster recovered at the short par-4 16t. She played a sand-wedge to six feet for birdie. At the 18th, Inkster's drive left her only 200 yards to the pin, and she reached the par-5 green in two with a 5-iron. She rolled home the short eagle putt to grab a piece of the first-round lead.
'I played really steady out there today,' said Inkster. 'I made one bad swing on the par-5 but I had a lot of birdie opportunities. I hit a lot of fairways so I had a lot of putts at it.'
Samantha Head is in sixth place after an opening-round 69, followed by a group of nine players tied for seventh at minus-2. Among the notable players in the group at 70 are former champions Laura Davies and Rachel Teske, Karrie Webb, Se Ri Pak and Kelly Robbins, who lost in the playoff at the U.S. Women's Open earlier this month.
Hilary Lunke, who shocked the golf world with her playoff win at Pumpkin Ridge, carded a 2-over 74 on Wednesday to finish in a logjam tied for 46th place.