American Oberholser, whose progress has been blighted by injury, made a flying start with four birdies from the opening six holes - including a superb 65-foot putt on the fifth – as he progressed to 11-under par overall.
Although he bogeyed the par-three eighth and 13th he was pleased with his display on the Raptor Course at Grayhawk Golf Club.
"I got into a good rhythm off the start and started striking the ball well from tee one, and really just hit a couple of wayward irons," he said. "Other than that, my driver was really good today. I hit 14 fairways.
"I could make some improvements, but I putted well. There were all the ingredients you need to shoot a 64."
Americans Brad Elder and George McNeill are a shot behind Allan on nine-under after both shot rounds of 63. Paul Goydos shot the best round of the day with his eight-under 62 putting him back in contention after his even-par 70 on Thursday. He is three-behind Oberholser in a tie for fifth.
Overnight joint leader John Mallinger who shot seven-under on Thursday, recovered from a poor front nine, where he was two over, to make a one-under 69.
The other leader from Thursday, Doug LaBelle II, was two over on Friday with a double bogey on the par-three 16th spoiling his round that was mixed with three birdies and another three bogeys.
Last year's winner, Canadian Mike Weir, the highest ranked player in the field at 22, is five shots behind Oberholser.