On the first day of play this season on the Champions Tour Cochran gave himself a chance to produce what would have been the first 59 in the history of the over-50 circuit.
He played the first six holes on the back nine of the Hualalai Golf Club course in 6-under and that got him to 10-under for the round. Birdies on the final three holes would have brought him the 59, but he had to settle for pars on each one.
Nevertheless, he put himself in position for a third victory on the Champions Tour.
Cochran had a one-shot lead over defending champion Tom Watson and Ben Crenshaw, who turned 59 this month, and who has never won on the Champions circuit. This was Crenshaw's lowest score ever on the tour.
Watson is winless since his victory on this course last year.
Mark McNulty, Jeff Sluman and last year's leading money winner Bernhard Langer were all at 65. Tom Lehman, Mark O'Meara and John Cook each shot a 66.
Of the 42 players in the elite field, 13 have won a major championship on the regular tour.