The Blues secured Champions League qualification last week and Maurizio Sarri made changes after his side needed penalties to down Eintracht Frankfurt in the Europa League semi-final.
Gonzalo Higuain missed the best chance to break the deadlock at the King Power Stadium, but Chelsea ended the campaign above Tottenham after the Champions League finalists drew 2-2 home to Everton.
Kasper Schmeichel made a great reaction block to deny Ross Barkley in the third minute before the Leicester goalkeeper dived low to his left to keep out Willian's tame effort.
James Maddison and Higuain fired off target in a first half played at low tempo but Leicester should have struck first, Jamie Vardy playing a poor pass at the end of a quick break.
Chelsea wasted an even better chance to open the scoring on the stroke of half-time, Higuain making a mess of a seemingly straightforward opportunity created by Marcos Alonso.
Barkley pulled a shot wide after the restart before a crucial Cesar Azpilicueta intervention prevented Vardy from having a clear sight of goal.
Sarri brought on Eden Hazard with 21 minutes to go while Leicester introduced title-winning duo Shinji Okazaki and Danny Simpson for farewell appearances.
But, with little riding on the result, the match petered out, although Youri Tielemans shot over late on, Chelsea's attention having seemingly turned to their Europa League final against Arsenal in Baku.