Choi and Appleby both fired a 67 at the Congressional Country Club to reach 7-under 133 at the midway point.
Woods -- the host of the tournament -- entered the second round in danger of missing the cut, but he shot a 66 Friday and moved into a share of 12th place at 139. Woods, playing for the first time since he became a father, made three straight birdies to close his round.
"I hit it about as good as I did yesterday," Woods said. "Only difference is I made a few more putts."
Choi is seeking what would be an impressive double in tournaments with golf superstars as hosts. Earlier this year he won The Memorial Tournament, an event created by Jack Nicklaus.
Phil Mickelson, who seemed likely to play on the weekend until he double bogeyed two of his last three holes, was among those who missed the cut Friday.