Kobayashi set the fastest lap of three minutes 15.497 seconds in the second of three qualifying sessions at the Sarthe circuit.
The Japanese, who shares the number seven car with Britain's Mike Conway and Argentine Jose Maria Lopez, has yet to win the French endurance classic but has now twice secured pole position.
Spain's double Formula One champion Fernando Alonso, Switzerland's Sebastien Buemi and Japan's Kazuki Nakajima won last year and again share the number eight Toyota with their eyes also on winning the overall world endurance championship.
Nakajima set their fastest lap, 0.411 slower than Kobayashi, in second place.
Russian Egor Orudzhev secured third spot on the grid for the number 17 non-hybrid SMP Racing car.
The next on-track action will be a Saturday morning warm-up before the start at 1500 local (1300 GMT).
(Reporting by Alan Baldwin, editing by Ed Osmond)
