The Hoops started playing due to the fact that they could lead to the lead after the Hearts' Kilmarnock defeat.
CELTIC climbed to the table for the first time this season with a free-throw draw in Livingston.
The Brendan Rodgers men were able to compete with Kilmarnock's leader, Hearts.
Hope, who won 2-1 against Thursday night RB Leipzig, had two clashes at Tony Macaroni Arena.
Scott Bain and Kristoffer Ajer replaced Craig Gordon and Filip Benkovic, who were injured.
Ryan Christy had the best opportunity in the first half but Livi No1 Liam Kelly was rejected.
Going home Patrick Roberts cuts his loan order from Girona and returns to Man City.
Scott Bain has been moved to final action several times.
Both teams, however, could not break the deadlock because both teams took over the spoils.
Gary Holt's men lost their second consecutive victory with a good record against the Scottish champions.
However, while Chelsea is returning to the Premier League's goal-break summit, Parkhead will be disappointed that he has not given up all three points.
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