ceded top spot in Champions League Group C to Roma as the Italians beat Antonio Conte's side 3-0 on Tuesday evening.
The Blues were soundly beaten at the Stadio Olimpico, with Stephan El Shaarawy opening the scoring after 38 seconds with an exquisite first-time volley.
El Shaarawy added a second just after the half-hour mark, before Diego Perotti rounded off the victory with a fine long-range strike midway through the second half.
The result moves Roma top of Group C, one point ahead of Chelsea, who will be thankful Atletico Madrid failed to beat Qarabag at home to ensure their chances of qualifying for the knockout stage of Europe's premier competition remain on course.