+Kirkland's score of eight under par gives her a slender one-shot lead over compatriot Virginie Lagoutte-Clement and Finland's Kaisa Ruuttila.
Lagoutte-Clement had led for the majority of the day, but a round including nine birdies and a bogey put Kirkland at the top of the leaderboard.
Ruuttila shot an eagle on the 18th to climb into joint second.and put her above Norway's Marianne Skarpnord who is two shots back in fourth.
There is a three-way tie for fifth between Spain's Tania Elosegui, Australian Stacey Keating and England's Sophie Walker, who are all five under par.
Elosegui shot eagles on the seventh and 18th holes but a bogey on the 12th left her three shots behind the leader.
Further down the scoreboard, there was a 10-way tie for 13th place, five strokes off the lead.