The trio carded five-under-par 67s on the Sandbelt Course, giving them a one-shot advantage over the chasing pack.
Five players make up that group, with world number four Inbee Park one of them.
England's Holly Aitchison is one of six players a further shot back, although Scottish amateur Eilidh Briggs had a day to forget as she signed for a nine-over 81.
"I think in rounds like today [Thursday], you have to limit your mistakes and try not to have any three-putts and take your chances," joint-leader Walker told the tournament's official website.
"Today's [Thursday] round was pretty impressive. If I can do that again then I'm sure I'll be close but I'll take every round as it comes and try and eliminate the mistakes."