The draw lifted Chelsea to 71 points, 19behind leaders Manchester City and three ahead of London rivals TottenhamHotspur in fourth, but Chelsea"s far superior goal difference means Spurs haveno realistic chance of overtaking them.
Chelsea will be disappointed not to win agame in which they had 27 shots but scored only one goal as they dominatedpossession.
In contrast, Leicester scored with theironly effort on target after seven minutes as Kasper Schmeichel sent a sweepinglong ball to Timothy Castagne and his deflected pass fell into the path ofJames Maddison who curled a shot past Edouard Mendy.
Chelsea"s 34th-minute equaliser was exquisiteas Reece James lofted a diagonal ball into the area for Alonso to volley homeand it looked a matter of time before they added to their tally.
Thiago Silva sent a raking ball into thebox but the lively Hakim Ziyech could not connect with it as Chelsea sought toturn their dominance into goals.
They earned a number of corners and freekicks around the area and though Leicester"s loose defending at set pieces hasproved costly all season, Schmeichel was quickly off his line to claim the balland avert danger.
Christian Pulisic missed a glorious chanceto bag the winner for Chelsea, completely miscuing his shot from RomeluLukaku"s ball across the face of goal and sending his effort wide.
"We were the better team and deservedto win, we didn"t allow any chances, got punished by a shot from outside thebox," Chelsea manager Thomas Tuchel told reporters.
"We created enough to win, didn"tallow transition and chances for Leicester, so I am fine with the performance.
"It"s a bit of a broken record - wedid not take what we deserve."
Chelsea round off their league campaign athome to relegated Watford on Sunday when Leicester, who are in ninth place on49 points, host Southampton.
