Thomas Tuchel is now 12 games without defeat since being appointed manager, but his team were pushed all the way at Elland Road on Saturday.
A 0-0 draw is a far reflection on the performance, leaving Chelsea in fourth place and are two points off third-placed Leicester City who have a game in hand. If West Ham, Everton and Tottenham win their two games in hand, the Blues could drop to seventh.
Leeds saw an early effort from Tyler Roberts correctly ruled out for offside and then Chelsea came close thanks to a mess up in the Leeds defence, Luke Ayling hitting a clearance into team-mate Diego Llorente with the ball spinning back towards the hosts’ goal and hitting the bar.
Chelsea keeper Edouard Mendy did well to tip a curling shot from Roberts against the bar and had to be on alert several times after the break.