Kaleka had a stretch of four straight birdies on St. Andrews as he looks to secure a first tour victory and continue the recent streak of success for French golfers.
"It's been a great month for French golf with Gregory Bourdy winning the Wales Open and Julien Quesne winning last week's Italian Open," the 26-year-old Kaleka said. "But today was very special for me as I have played the Old Course many times before as an amateur in the St. Andrews Links Trophy but this 64 is my lowest round."
Another five players are tied for sixth, one shot behind, including recent Johnnie Walker Championship winner Tommy Fleetwood.
Former Dunhill champion Nick Dougherty of England was in last place after needing 12 strokes on the par-4 18th hole at Carnoustie, which the 2007 winner was playing as his ninth.
Dougherty was already 3 over par and proceeded to put two balls out of bounds on the 18th and signing for an eventual round of 86 that left him 7 shots behind the nearest golfer.
Former U.S. Open champion Michael Campbell of New Zealand was forced to withdraw from his third straight event after badly twisting his ankle on the sixth at Kingsbarns. A bout of food poisoning had forced Campbell out of the European Masters, and he then withdrew a week later after one round of the KLM Open.