The 27-year-old Dane, playing in his first PGA, lofted a 6-iron shot that bounced once on the green and then dropped into the cup for a hole-in-one.
The shot left the world number 44 at two-over par. He closed with a bogey at 18 for a three-over 73 and a three-over total of 283, tied for 19th when he walked off the course.
It's the fifth major start for Bjerregaard, who missed the cut in the 2011 British Open and 2015 US Open, shared 40th in the 2014 US Open and shared 21st in last month's Masters.
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