The third-placed Blues moved four points ahead of both Leicester in fourth and Manchester United in fifth, with their final two Premier League matches against champions Liverpool and high-flying Wolves.
Norwich were unable to generate any clear-cut chances, but manager Daniel Farke still hailed the commitment of his Canaries, who had seen their relegation confirmed with a 4-0 thumping by West Ham.
"I have to say I am pretty pleased with the reaction of my lads," said Farke.
"We had to deal with the disappointment against Chelsea's need to win this game.
"And I think we were unbelievably competitive, really compact and not that far away from winning a point."