Briton Jimmy Mullen, the overnight leader, dropped back after a 74 at Carnoustie.
"It was a great day. I started off badly by hitting it in the water on the first but I got over it and played some good golf out there," said Olesen, who was runner-up at the pro-am event three years ago.
"My putter started to get very hot out there and I holed a lot of great putts. So yeah, it was good fun."
The tournament, which concludes on Sunday, is a unique format with four balls made up of two professionals and two amateur players alternating between links courses at Kingsbarns, Carnoustie and the Old Course at St Andrews.
Frenchman Benjamin Hebert carded six birdies in a round of 67 at Carnoustie and is in third place, four shots back.
(Reporting by Martyn Herman; Editing by Mark Lamport-Stokes)
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