Hazard impressed during the draw with Liverpool at Anfield on Saturday but is one of four players who started on Merseyside left out by Antonio Conte.
Danny Drinkwater and Tiemoue Bakayoko both join Hazard in dropping to the bench, with Cesc Fabregas, Pedro and Willian recalled to the starting line-up
Cesar Azpilicueta, meanwhile, is replaced by Antonio Rudiger, bringing to an end a run of 74 successive Premier League starts for the Spain international.
74 - Cesar Azpilicueta isn't starting a Chelsea PL game for the first time since December 2015, having played 90 minutes in each of the Blues' last 74 top-flight matches. Dave. pic.twitter.com/sC3WXW65o2— OptaJoe (@OptaJoe) November 29, 2017
He has played every minute of those games, with Wednesday's clash the first time he has missed out since December 2015.
Victor Moses remains on the bench, with Davide Zappacosta again preferred at right wing-back.
Chelsea starting XI: Courtois; Rudiger, Christensen, Cahill; Zappacosta, Fabregas, Kante, Alonso; Willian, Morata, Pedro. Subs: Caballero, Azpilicueta, Ampadu, Moses, Drinkwater, Bakayoko, Hazard.
Swansea starting XI: Fabianski, Naughton, Van der Hoorn, Mawson, Olsson, Ki Mesa, Carroll, Renato Sanches, Bony, Ayew. Subs: Fer, Dyer, Nordfeldt, Routledge, Clucas, Rangel, McBurnie.