England's Tommy Fleetwood (11 under) is one shot off American Brian Harman's lead.
Laird was the only Scot to make the cut at the Erin Hills course in Wisconsin and will start his fourth round with South Korean Whee Kim at 17:36 BST.
Richie Ramsay, at two over, missed the cut by one shot and Scottish compatriot Russell Knox was five over.
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Martin Laird's ever-par 72 means he is one under going into his final round at the US Open.