The home side managed just one shot on target while Leicester managed seven.
Even the 68th-minute dismissal of Leicester defender Ben Chilwell for two bookings couldn't lift lethargic Chelsea, who were outplayed in the first half and couldn't make their numerical advantage count at the end of the second period.
The Gunners themselves play on Sunday afternoon when they face a trip to Bournemouth, just over twelve months after their last visit to the Vitality Stadium - arguably one of the games of last season.More news: Former Texas A&M head coach Kevin Sumlin to be hired at Arizona
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Asked whether the Chelsea board has considered bringing the Englishman to Stamford Bridge, Conte said, "No, honestly we didn't speak about him, but I repeat we are talking about a really good player". "This shows we have a good player".
The Belgian internationals future has been the subject of intense speculation recently with Real Madrid said to be monitoring his contract situation closely, and the Spanish giants may well feel that comments like these suggest he may not be completely happy with life at Stamford Bridge.
"I think it's a good thing if he continues the season with us".
The Chelsea manager admitted that the strains of the midweek Carabao Cup semi-final against Arsenal at home had taken its toll on his players. I saw a lot of players very exhausted. But we deserved the point and perhaps more with all the chances we had. If they start shouting it doesn't help us.
Chelsea head coach Antonio Conte rotated his options for last week's FA Cup third-round tie at Norwich and can be expected to do so for this Wednesday's replay.