Leeds United came closest to scoring with Tyler Roberts having a goal disallowed and another effort hitting the woodwork, while Diego Llorente cleared into his own crossbar as well.
It was another clean sheet for Chelsea goalkeeper Edouard Mendy, with the Blues having not conceded in their past five matches in all competitions.
“We could have won,” Chelsea boss Thomas Tuchel said. “We created enough chances and enough touches in the box to score one or two goals. Unfortunately, we didnt, so we have to live with a draw.
“The pitch was super hard to play on, slippery and bouncy. We had a couple of chances to go ahead that we didnt take, and then Leeds put some pressure on us and they troubled us at times.
“It was an absolutely okay away game against a team that put pressure on you. We found situations where we could escape the pressure, have high recoveries of the ball, but we were not clinical enough in our counter-attacks. We take a 0-0.”
Elsewhere, Manchester City won 3-0 at Fulham, with Sergio Aguero back among the goals which were all scored within 15 minutes in the second-half.
“Of course its important. For him goals are everything,” City boss Pep Guardiola said.
“Everybody wants to jump on the bus, he is more than welcome. It was so important his goal - he played 90 minutes for the first time in a long time.”
Crystal Palace beat West Bromwich 1-0 leaving the Baggies destined for the drop, while Burnley shocked Everton 2-1 at Goodison Park.