The American holds a one-shot lead over 57-year-old compatriot Mark O'Meara and Spain's Rafael Cabrera-Bello, who both carded 67.
Next came a group of five players -- Americans Dustin Johnson, Brandt Snedeker and Tom Lehman, Miguel Angel Jimenez of Spain and India's Shiv Kapur -- on three under.
American teenager Jordan Speith, who beat Zach Johnson and David Hearn to the John Deere Classic title in a play-off earlier this month, joined Woods on two-under.
That victory earned the 19-year-old the last spot in the British Open and the debutant is in relaxed mood at Muirfield.
"It has been a great couple of weeks," Speith said. "I've kind of accomplished more than I'd thought possible this year."
What wouldn't McIlroy give to be able to say the same thing?