The Blues dominated possession in the first half but were largely frustrated by a disciplined Everton side, well drilled by Marco Silva who had clearly done his homework on "Sarriball".
The 32-year-old has only played six times for Chelsea this season, with new manager Maurizio Sarri preferring David Luiz and Antonio Rudiger as his centre-back partnership in the Premier League. One of the main aims of Sarri's style is to draw the opposition line out and create space behind the defence.
Liverpool won against Fulham and Manchester City defeated rivals Manchester United at the Etihad Stadium.
Alvaro Morata got into some great positions against Everton, as he often does, but was so wasteful and lacked composure in the final third, also finding himself offside when he eventually did put the ball in the back of the net.
With Everton allowed to keep 11 men on the field, Chelsea were unable to break the Toffees down and had to settle for a share of the spoils.
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Your goalkeeper can be the most important player in that regard and, today, Jordan Pickford was well up to the task. I guess when I am on the floor I can win free-kicks so every free-kick with Chelsea is a chance to score more goals.
"I am not happy with being kicked to be fair but it's part of football". The clash saw both players go to the book and with the incident having been dealt with at the time, it sees further retrospective action ruled out.
He did not discuss his future on this occasion, looking only at the opportunities for Chelsea.
"The referee tries to do his job and I try to do mine".
Chelsea's next game, following the global break, is away to Tottenham, with the German defender hopeful the Blues can avoid dropping further points as they look to keep in touch with those at the top of the table.