The Japanese driver, in the number seven TS050 hybrid car shared with Britain's Mike Conway and Argentina's Jose Maria Lopez, lapped the Sarthe circuit with a best time of three minutes 17.161 seconds.
Conway was involved in drama later in the two-hour session when he was in a frontal collision with the number 31 Dragonspeed LMP2 car that had spun off with Mexican Roberto Gonzalez at the wheel.
Neither driver was injured and both cars continued after repairs.
SMP Racing were second fastest, with Russian Egor Orudzhev 0.472 seconds off Kobayashi's pace in dry conditions in the number 17 car he shares with compatriot Sergey Sirotkin and Frenchman Stephane Sarrazin.
The number three Rebellion Racing car was third on the timesheets with French driver Thomas Laurent setting their fastest lap some 2.4 seconds slower than the leading Toyota.
Last year's winning trio of Spaniard Fernando Alonso, Japan's Kazuki Nakajima and Swiss driver Sebastien Buemi, who also lead the world endurance championship, were fourth fastest in the number eight Toyota.
Final qualifying for the 62-car race, whose 87th edition starts on Saturday, is on Thursday evening with two more sessions.
Toyota, the only major manufacturer in the top LMP1 category, are favourites to retain their title on Sunday.
(Reporting by Alan Baldwin, editing by Ed Osmond)
