The 24-year-old needs to win in Quail Hollow this week to become the youngest man in the history of the game to secure all four majors, but sits five strokes off the pace after the first 18 holes.
The Texan carded a one-over-par 72 and joined Northern Ireland's Rory McIlroy in being just the wrong side of par.
Kevin Kisner and Thorbjorn Olesen share the lead on -4 after a tough day for the field in testing conditions, with the greens lightning fast and birdies at a premium.
There are a number of stars between the leaders and Spieth, with Dustin Johnson, Jason Day and John Rahm on one-under par, while Patrick Reed, Paul Casey and Rickey Fowler are a shot better off, and the Open champion knows he needs to close the gap as soon as possible to stand a chance of contending on Sunday.
"Historically, I'm pretty solid with the lead," he said. "It's much easier when you are on the front page of the leaderboard than it is coming from behind. "Given it's the first round, I know I'm still in it but I know that tomorrow's round becomes that much more important to work my way and stay in it.
"I've got to make up ground. I can't putt any worse than I did today. I burned a lot of edges. Some were good putts and some weren't."