The Dane, who won this season's Irish Open, shot a bogey-free round on another day of low scoring at the par-70 Kennemer Golf and Country Club. Kjeldsen is one shot ahead of Wade Ormsby of Australia - who followed his 61 on Thursday with a 68 - and England's David Horsey (66).
''You have to enjoy the days when things are going well,'' Kjeldsen said. ''As you know, in golf we get all sorts, but today was another great day.''
Matthew Fitzpatrick left a birdie putt just short on his final hole to miss out by the narrowest of margins on the first 59 on the European Tour.
The 21-year-old Englishman started his round on the 10th tee and shot six birdies on the back nine then followed it up with four more on the front nine for a 60.
Fitzpatrick was already thinking about the possibility of a 59 after his storming first nine holes.
''To give myself a shot at that magic number was great,'' he said. ''Shame that putt at the end came up short but I'll take 60 any day of the week.''
Fitzpatrick, ranked 114th in the world, was the best amateur at the 2013 British Open and turned pro the following year. His round left him three strokes off the lead.
''Everything went right. I had a nice bit of luck occasionally and putted really well,'' Fitzpatrick said.
Tom Watson birdied the par-3 17th for a 68 that ensured he would be around for the weekend.