Finch, who won the Irish Open in May, birdied five of his first seven holes and had four birdies on the back nine.
Its the first time I played the tournament and I am glad I just gave myself a chance, he said.
Robert Karlsson followed the leaders with a 67. He is one of four European players using the tournament to warm up for next weeks Ryder Cup in Louisville, Ky.
Ross Fisher was at 68, with Anders Hansen and James Kingston at 69. Defending champion Soren Hansen, another member of the Ryder Cup team, shot a 73. He is trying to become the first player to win this title in consecutive years.
The two other European Ryder Cup players at this tournament are Graeme McDowell and Miguel Angel Jimenez, and both shot 72.
Fred Couples and John Daly started strong but faded. Couples (75) made an eagle on his first hole and a birdie on his second. Daly (73) birdied his first two holes.
Retief Goosen, the 2005 champion, shot a 76, and four-time champion Bernhard Langer was at 70.