Choi equaled the day's lowest round at the Westchester Country Club with a 5-under 66 that left him at 12-under 130 in the first of the four tournaments that make up the tour's inaugural season-ending playoff.
Woods, who began the week with a 1,000-point lead over Vijay Singh, skipped this tournament -- leaving him vulnerable to losing his advantage. A win by Choi would give him a 6,500-point cushion over Woods.
Choi had a two-shot lead at the 36-hole mark over former PGA champ Rich Beem, who began the week ranked just 134th on the FedEx Cup list.
Phil Mickelson was among those at 137. Singh failed to take advantage of Woods' absence and missed the cut. The leading 120 players on the points' list advance to next week's tournament in Boston.