Claxton, trying to gain exempt status on the PGA Tour for the first time, has led this grueling event after each round to date. He stood at 13-under 203.
The 171-player field will alternate in competing over the Nicklaus Tournament Course and the PGA West-TPC Stadium Course. The top 25 after 108 holes will earn their way onto the tour for next season.
Bobby Gates, Matt Jones and Seung-yul Noh, who shot the day's low round of 64, were Two shots behind Claxton.
Billy Hurley, a graduate of the U.S. Naval Academy who has just fulfilled his five-year military commitment, and two-time PGA Tour winner Vaughn Taylor were tied for fifth at 206.
Of the four major championship winners in the field, 2002 PGA champion Rich Beem was in the best position. He shot a 67 to move into a share of 33rd place at 211. He is only one shot out of the top 25.