Stadler is nine-under-par 135 after 36 holes and leads by one over Jay Haas.
Haas, who was picked to the United States Ryder Cup team, shot a six-under 66 and is at eight-under-par 136.
Tom Kite, who won the 1992 U.S. Open at Pebble Beach, and Hale Irwin, each posted rounds of six-under 66 and are tied for third place with D.A. Weibring (71) and Gary McCord (68). That group is knotted at five-under-par 139.
"This game is so much fun when you're making putts," said Stadler. "I darn near made everything today. This is my best round here. I'm looking forward to tomorrow."
Notable deaths of 2014 [PHOTOS]