The native of Northern Ireland leads Stuart Appleby (65), who won for the second time this season at the Shell Houston Open last weekend.
Two-time U.S. Open champion Retief Goosen leads a group in third place at 6-under 66. He was joined there by Nick Watney, Stuart Deane, Bubba Watson, Robert Garrigus, Lucas Glover, Tommy Armour III, Olin Browne, Charley Hoffman and Jeff Sluman.
Phil Mickelson, playing for the first time since winning his second Masters title, started with a 4-under-par 68 and is tied for 22nd place.
The Zurich Classic is one of the first major sporting events in New Orleans since the Gulf region was hit by Hurricane Katrina last year.