Leicester coach Brendan Rodgers decided to stick with the same starting XI that lost to Manchester City on Monday, while Chelsea boss Maurizio Sarri made five changes to his side as he focuses on the Europa League.
The Blues made a flying start to the game but Ross Barkley was denied after a save from Kasper Schmeichel in the third minute.
Barkley beat the offside trap but he could not fire home from a close angle, with Schmeichel tipping the ball away with his shoulder.
The Dane was then on hand to thwart Willian before Leicester finally started to come into the game. Ben Chilwell was denied by Willy Caballero in the 17th minute, before the former Manchester City keeper denied both James Maddison and Youri Tielemans.
The best chance of the game fell to Gonzalo Higuain on the stroke of half time but the Argentinean scuffed his lines at the pivotal moment.
Marcos Alonso’s cross was inch perfect but Higuain fell over the ball as he tried to backheel his shot into the bottom corner.
So much was expected in the second half but neither side settled into their rhythm. Tielemans tried his luck from range in the 48th minute but the Monaco man watched on as his shot fired past the post.
Barkley went close just five minutes later but the former Everton man dragged his shot wide after finding space in the box.
Neither team went close in the final 30 minutes, with Rodgers taking the opportunity to give Shinji Okazaki and Danny Simpson some game time before they leave the club in the summer.
Leicester failed to secure eighth spot, but Chelsea can now look forward to the Europa League final after clinching third.