Olesen set the early pace and carded a commendable 67 to put pressure on the rest of the field as many struggled at Quail Hollow.
Only 24 players managed to break par and Olesen thought he had done enough to lead going into the second round.
However, Kisner rallied and birdied three of his last five holes to give himself a solid start to the tournament.
Brooks Koepka, Chris Stroud, DA Points, Gary Woodland and Grayson Murray are all tied in third on three-under but Olesen admits he is feeling positive this week.
He told reporters: "I've had a couple of top-10s in majors and I feel like I've learned a lot over the years playing quite a few majors now.
"I feel like I'm better prepared to be in contention over the weekend and have a chance to win."