Their double substitution with less than an hour on the clock highlighted the home side's struggles to find a way through this Leicester defence - even tired, those two had been Chelsea's most likely route towards a goal against the run of play in a first half dominated by the Foxes.
Meanwhile the Foxes have consolidated their hold on ninth place in the league and continue their impressive run under Claude Puel.
1' - We are underway at Stamford Bridge!
With rumours surrounding his future, Riyad Mahrez did his stock no harm with an impressive display against Chelsea.
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Courtois' feelings towards being booed are understandable, but when you've drawn three consecutive games 0-0, it's easy to see why Chelsea fans are agitated. We played the game against Arsenal on Wednesday night and didn't have a lot of time to recover.
One man who would have been rubbing his hands following the game is Norwich City boss Daniel Farke.
With both sides still face in the semi-final of the Carabao Cup on the 10th and 24th of January, it is almost certain that Arsenal who will welcome back most of their key players who missed the Wednesday league clash will somehow get the better of Chelsea.
Conte has also criticised United's spending, while Mourinho even mocked the Chelsea head coach for having a hair transplant. But when they struggle, Antonio Conte does not have a Plan B or C to rescue them.
Chelsea were poor for large parts of todays game, and Leicester dominated proceddings at times.
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"I think a lot of our players were exhausted".
With no end to the fixture crunch in sight, Conte must hope the hamstring injury suffered by Gary Cahill is not severe. Cesc Fabregas twice tested Kasper Schmeichel, with Chelsea's two best opportunities but the blues looked out of ideas and couldn't find the breakthrough.
The enmity between the two men stretches back to early last season, with Mourinho accusing Conte of humiliating him with the scale of his celebrations as United fell to a 4-0 defeat at Stamford Bridge in October 2016.
Chilwell was booked for a foul on Willian, and five minutes he later picked up his second yellow card after catching Victor Moses.
Jan 7: Conte said: "When there are comments where you try to offend the person and don't know the truth, then you are a little man".
Rafa Benitez locked in transfer stand-off with Mike Ashley
He (Ashley) knows he has to improve the team so that we have the quality which allows us to stay in the Premier League . I have heard people talking about our players, but we do not have any offers.