Defending champion J.B. Holmes also made a good start to his campaign as hit a 69, but world number one Rory McIlroy remained five strokes behind Streb as he endured a turbulent round.
Streb was on song throughout the day as he tamed the difficult Quail Hollow course with seven birdies.
The 28-year-old's putting was a sight to marvel at as he sunk a number of difficult putts, including an exceptional 35-footer on the 17th, an excellent 19-footer on the 11th and a lovely 15-footer on the second.
One stroke behind Streb is the American duo of Patrick Reed and Kevin Chappell, who both hit first rounds of 66.
Reed started with a bogey on the first before hitting a birdie on the second, which came courtesy of a brilliant 36-foot putt.
This seemed to fire Reed up as he rounded off his front nine with five birdies, including four in a row from the fifth to the eighth.
Reed continued his stellar performance with birdies on the 10th, 14th and 15th before letting himself down at the end with a bogey on the par-three 17th.
Like Reed, Chappell began with a bogey on the first before finding his stride with a birdie on the fourth, an eagle on the par-five seventh, which came as a result of a 37-foot putt, and a birdie on the eighth.
His consistency and excellent putting carried on into the back nine as he hit three more birdies, which included a 29-foot putt on the 10th.
Sitting two shots behind Streb are Webb Simpson, Ricky Barnes, Michael Thompson, Stewart Cink, Chesson Hadley and Billy Hurley III as they all hit first-round 67s.
McIlroy finished tied 30th following his first round 70, which saw him start with a birdie on the first and a disappointing bogey on the second.
But, he bounced back with two more birdies on the fifth and seventh to round off his front nine.
The Ulsterman's back nine was exactly the same as his front nine, except for the double bogey on the 17th, which occurred when he missed an eight-foot putt.
Holmes was more successful than McIlroy as he recorded a first round 69, which included four birdies and a bogey, to trail Streb by four strokes.