Parker, the 2010 champion, put herself firmly in the hunt once again with a 68, responding to an early bogey with five birdies.
Starting on the back nine, the English player dropped a shot at the 12th but then birdied three of the last five holes on the back nine. Two more birdies at six and seven saw her join the leaders.
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Hide AdOf the three Scots in the field, Kylie Walker (71) and Clare Queen (72) are well placed, but Vikki Laing was way down the leaderboard after shooting 80.