Olesen, 22 and looking for his first European Tour victory, had five front-side birdies en route to a second-round, 5-under-par 67. He is at 7-under 137 after 36 holes.
Matteo Manassero, whose 7-under 65 was the round of the day, is tied with Gareth Maybin for second at 6-under. Maybin shot 70.
Tiger Woods had a 3-under 69 in the second round and is in a group of seven players tied for fourth at 5-under. That group includes first-round co-leaders Robert Karlsson and Rory McIlroy, who turned in even-par 72s in the second round.
McIlroy's round included a double bogey at the third hole and a two-stroke penalty that gave him a 6 at the par-4 ninth hole. McIlroy was penalized for brushing away sand that wasn't on the putting surface.
Olesen opened with three birdies in his first four holes but slipped with a bogey at No. 5. He put together four more birdies over Nos. 8-12 before a bogey at the par-5, 567-yard 18th.
Biologists detail four new deep-sea 'killer sponges'
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend