Simpson, who plays at Quail Hollow Club at least once a week when he is at home, used his extensive course knowledge to card a five-under-par 67 and join first-round leader Streb (69) at 10-under 134.
They were two shots clear of their nearest rivals while the two most celebrated players in the field, Rory McIlroy (67) and Phil Mickelson (66), vaulted into contention just three strokes off the pace.
Simpson, the 2012 U.S. Open champion, chipped in from 55 feet at the par-four ninth, and provided an even more impressive encore from 65 feet at the par-three 17th.
"I don't think I've ever chipped in twice on tour in the same round," he told reporters before rushing off to his mother-in-law's birthday party.
"I can't imagine more support than today. If I'm (struggling) at any point early in the round tomorrow, I think that support will help me."
Simpson, who lives adjacent to the seventh hole, felt that his course knowledge helped his comfort level at the event.
"The best player is going to win this week, no matter how many times (he) has played it, but I definitely feel a little sense of comfort knowing I've been here so much," he said.
Earlier in the day, world number one McIlroy followed up his Thursday night comment that the course was "there to be had" by compiling five birdies in a bogey-free round.
MEDIOCRE IRON PLAY
The Northern Irishman said good driving had been the key to his score, but lamented some mediocre iron play that prevented him from piling up more birdies.
"Mentally I feel very sharp," he said. "I'm not putting myself under that much stress of having to save pars or anything."
McIlroy, 26, observed how much he has changed as a golfer since his maiden PGA Tour victory here five years ago.
"Everything has changed," he said. "I feel I'm a much better player. My stature is much higher. When I'm on the leaderboard, it carries a bit more weight.
"I'm much better prepared and equipped to be in contention week-in and week-out, more grounded and mentally much better as well."
Mickelson, meanwhile, was relieved to finally post a score that, in his opinion, reflected the quality of his performance.
The American left-hander also said he was "shocked" that he had never won at Quail Hollow, a course he believes suits his aggressive style.
"I'll have a good shot this weekend," Mickelson told reporters. "Hopefully I can break through."
(Editing by Mark Lamport-Stokes)
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