Walker carded his best round in a major championship, firing a 5-under 65 in the opening round today. He had six birdies and a bogey following an early tee time.
Walker is trying to become the fourth first-time major champion this year.
Martin Kaymer shares second with Argentina's Emiliano Grillo and England's Ross Fisher. Kaymer won the tournament six years ago.
Reigning British Open champ Henrik Stenson finds himself in a four-way tie for fifth with Andy Sullivan and Americans Harris English and James Hahn.
Defending champion Jason Day and Rickie Fowler each shot a 68, and Jordan Spieth came in with a 70.
Phil Mickelson, the 2005 winner on the same Baltusrol course, opened with a 1-over-71. Rory McIlroy shot a 74.