Fog and rain forced the suspension of the first round on Thursday. Players returned to the course early Friday morning to resume play.
Oberholser, a two-time winner on the Nationwide Tour last year, had a bogey- free round with seven birdies to take the lead.
Tiger Woods, who is making his first start since undergoing knee surgery in December, was 1-under par through nine holes and struggled to find the fairway on Thursday. Woods, who won this event in 1999, took to the back nine Friday morning and tallied a birdie at the par-5 18th to finish at 2-under-par 70.
John Morgan and Spike McRoy were two strokes off the lead at 5-under-par 67.
Larry Mize, Marco Dawson, Jonathan Kaye, Dennis Paulson, Bob Tway, Matt Gogel, Darren Clarke, Cameron Beckman and Patrick Sheehan finished one shot further back at 4-under-par 68.
Defending champion Jose Maria Olazabal was in a group at 3-under-par 69 that includes three-time winner Phil Mickelson.