Laird, 33, and American Patrick Reed shot five-under-par 66s, with Australian world number one Jason Day two strokes further back.
Rory McIlroy carded three birdies and three bogeys in his first 18 holes at Bethpage Black to lie at level par.
Open champion Henrik Stenson pulled out of the New York event because of an old knee injury after finishing three over.
Olympic gold medallist Justin Rose hit five bogeys in his two-over 73.
The Barclays is the first of four FedEx Cup events, with the overall winner earning $10m (£7.6m).
