Tiger Woods, making a rare post-major championship appearance, shot a 67 and was one of three golfers four shots off the pace.
Baird's best finish on the PGA Tour has been a second second at the 2001 John Deere Classic.
"You play and you hope you put yourself into a position to win," Baird said.
Woods has gone three starts without a win. He captured the Match Play Championship on March 2, tied for 15th at the Masters, finished 29th at the Deutsche Bank Open in Germany and 20th at the U.S. Open.
Woods got off to a flying start Thursday with five birdies on his first 10 holes.