James Maddison fired Leicester City into a sixth-minute lead from the edge of the penalty area before Marcos Alonso met a Reece James cross on the volley to restore parity on 34 minutes.
The hosts upped the ante after the interval with Romelu Lukaku heading wide, Christian Pulisic missing from close range and Antonio Rudiger being thwarted in a frenetic six-minute spell.
Further chances fell to Trevor Chalobah and James but the hosts were unable to find a winner.
The result takes Chelsea’s points to 71, three more than Tottenham Hotspur with the Blues boasting a superior goal difference.
Leicester City stay ninth with 49 points from 37 matches.
Chelsea coach Thomas Tuchel on Premier League match against Leicester City at Stamford Bridge on Thursday , he said ,”We were the better team and deserved to win.We did what was needed and got a point. We did not allow anything, no chances for Leicester, but we got punished with a shot outside the box.
We created enough to win, did not allow transitions or chances so I’m absolutely fine with the performance. It’s a bit of a broken record – we did not take what we deserved but I think it was okay what we did.
It’s the story of the season. We need an assist from a wing-back and a goal from a wing-back. You can see the numbers of our offensive players and you can see the numbers from the teams in front of us.
Still today was the day we secured third place, we have been all season in the top three and we have in mind where we come from. We had some obstacles to overcome and some circumstances around the club which was not easy so full credit to the team.
‘It is a big step in consistency for us and maybe it doesn’t feel like this because the gap is so big to the top two teams. We have stuff to improve and we are the first ones to admit that.”