Nine players, including defending champion Karrie Webb, share third place at 3-under-par 69. The others at minus-3 are Soo-Yun Kang, Mi Hyun Kim, Marianne Morris, Grace Park, Amy Read, Jenny Rosales, Rachel Teske and Anna Acker-Macosko.
Barrett began her day on the back nine at Locust Hill Country Club. She started quickly with back-to-back birdies from the par-5 11th. She climbed to 3-under with a 10-foot birdie putt at the par-3 15th.
She kept rolling when she drained a 20-footer for birdie at the par-5 17th. However, before making the turn, she stumbled with a double-bogey at the 18th.
Around the turn, Barrett played steady golf. She parred the first six holes before catching fire to close the round. She birdied the par-3 seventh from 10 feet out and followed that up with a tap-in birdie at the next.
Barrett made it three in a row to finish her round when she dropped a 6-iron within eight feet at the par-3 ninth.
'It was obviously a good round,' said Barrett. 'I got off to a great start. I made some really good pars on the front side for a while and then birdied the last three coming in. It was a real solid ball-striking day for the most part and a great putting day.'
Barrett is looking for her first win since the 1989 Mitsubishi Motors Ocean State Open, which was her rookie season.
'I was very naive and if I look back at the player I was then and the player I am now, I'm much better now,' Barrett said. 'I had a good week and I won and I thought that's kind of how it worked but it doesn't really work that way, especially now, 15 years later. I've been through a lot since then. I lost a couple playoffs and had some other chances to win, but not as many as I'd like.'
Eathorne started her day with three birdies on the front nine. She got going with a birdie at the third from four feet out and followed that up with another at No. 5. She notched her third birdie of the day at par-5 eighth after she chipped to two feet.
The Canadian had a tough back nine. She started with a chip-in birdie at the 11th to move to minus-4 however, she struggled to three straight bogeys after failing to get up-and-down on all three holes to fall off the pace.
Eathorne made a strong comeback starting at the 15th. She birdied that and followed the birdie at 15 by dropping a sand-wedge within five feet at the next to setup another birdie. She capped a run of three straight birdies at the 17th to move within one of the lead.
'I had seven birdies out there and also three bogies and the three bogies were in a row and I managed to come back with three birdies after that,' said Eathorne. 'I guess I'm impressed with myself because I didn't allow myself to let those three bogies get me and I think I maybe yelled at my caddie a little bit and got it off my chest and was good to go after that.'
Hiromi Kobayashi, Nicole Dalkas, Se Ri Pak, Amy Fruhwirth, Tammie Green and Silvia Cavalleri stand at 2-under-par 70.