The Blues, whose winless run now stands at four matches in all competitions, grew into the game after a disappointing first-half showing but could not find a way through.
Leicester, beaten in 12 of their most recent 14 meetings with Chelsea in all competitions, saw their task become even tougher when Ben Chilwell was dismissed with a quarter of the game to play, but they held on for a share of the spoils on another day of frustration for Antonio Conte.
The match may have ended goalless, but it was not for the want of trying as the sides managed a combined 17 attempts in the first half alone.
Jamie Vardy also squandered two half-chances in quick succession, hooking one attempt into the side-netting and scuffing another wide of the target, while Shinji Okazaki missed the mark from six yards.
A fatigued Chelsea were very much second best in the first half, showing just two changes from their midweek draw with Arsenal here, though they did have openings of their own through Eden Hazard and Cesc Fabregas.
The latter had an angled drive helped aside and a longer-range shot tipped over the bar by Kasper Schmeichel, who was also well positioned to keep out Hazard's weak effort.
Leicester, who headed into this match on the back of successive away defeats in the top flight, continued to show more energy but were unable to find a way through before the teams went in for half time.
There was no change to the flow of the match in the opening 15 minutes of the second half, either, as the Foxes controlled possession and looked to get Vardy and the lively Riyad Mahrez on the ball.
Mahrez showed glimpses of what he is capable of throughout the afternoon, but his performance was soured somewhat when taking a dive just short of the hour mark, with retrospective action possibly to follow.
Conte was cutting a frustrated figure on the sidelines, being forced to use the last two of his changes - having lost Gary Cahill to an early injury - by bringing on the fresh legs of Pedro and Willian.
Willian, surprisingly left out once again today, made an instant impact with his pace down the flank, leading to bookings for Chilwell and Okazaki.
The Chilwell caution would prove pivotal as the full-back was yellow-carded for a second time four minutes later, this time for an over-the-ball challenge on Victor Moses that left his side down to 10 men.
Chelsea, boasting that impressive record against the Foxes - just one league loss here in 26 games - began to rack up the shots on target as former City ace N'Golo Kante and Willian both asked questions of Schmeichel.
Despite seeing far more of the ball in the closing stages, however, the champions ultimately struggled to create much and therefore missed out on the chance to climb into second place.
CHELSEA (3-5-1-1): Courtois; Azpilicueta, Cahill (Christensen 33'), Rudiger; Moses, Bakayoko, Kante, Fabregas (Willian 58'), Alonso; Hazard (Willian 58'), Morata
LEICESTER CITY (4-4-1-1): Schmeichel; Amartey, Dragovic, Maguire, Chilwell; Mahrez, James (Iborra 90'), Ndidi, Albrighton; Okazaki (Fuchs 73'); Vardy (Gray 82')