Cochran, the 2010 tournament winner, is making his first start since the US Senior Open in July.
Steve Pate, Andrew Magee, Fred Funk and Jay Don Blake were a stroke back. Funk, the Insperity Championship winner in May, missed a birdie putt on 18 by inches that would have given him a share of the lead.
“I had a really efficient front nine,” said Funk, who made the turn with a 30. “I got everything out of that front nine. Obviously, shooting five-under’s great. I’m playing really good. I’m playing solid, close to playing really, really good, and it’s more — it’s fun just to play.”
Magee extended his streak without a three-putt to 190 holes, the third-longest run on the Champions Tour this year.
Defending champion Kenny Perry and Bernard Langer topped a group at 68.