The Toffees remain unbeaten in six competitive matches this season, but face a tough task on Sunday as they travel to Stamford Bridge.
But can they do enough to shock the Premier League champions and continue their fine start to the campaign?
Seamus Coleman is unlikely to feature until around Christmas after the broken leg he suffered playing for the Republic of Ireland against Wales in March while fellow defender Ramiro Funes Mori is set for nine months on the sidelines with a knee problem.
Yannick Bolasie will also not feature until the new year at the very earliest as he continues to build up his fitness following two operations on a cruciate ligament injury.
Ross Barkley has suffered a further injury setback after picking up a hamstring problem that could sideline him for around a month, though with the England international keen on leaving Goodison Park, he may have already played his final match for the Toffees.
Summer signings Sandro Ramirez and Davy Klaassen both missed Thursday's clash with Hajduk Split and face a race against time to be fit for Sunday's game.
POTENTIAL STARTING LINE-UP
After marking his full debut with a stunning strike against Hajduk Split, Gylfi Sigurdsson will likely make his first Premier League start for the Toffees.
Mo Besic could deputise for Schneiderlin in midfield while Dominic Calvert-Lewin will likely lead the line again after impressing against Manchester City.
CHELSEA TEAM NEWS
Eden Hazard is moving ever closer to full fitness and could feature within the matchday squad following the ankle injury picked up early in pre-season.
Cesc Fabregas will return having been suspended against Tottenham while Pedro could start after coming off the bench to lay on the winner for Marcos Alonso at Wembley.
Fabregas's availability means David Luiz could drop back into defence, with Andreas Christensen likely to make way should that come to pass.
BEST OPTA MATCH FACTS
Chelsea are unbeaten in their last 22 home Premier League games against Everton since a 0-1 loss in November 1994 (W12 D10). Only against Tottenham (25) are they on a longer unbeaten Premier League run at Stamford Bridge.
Chelsea haven’t lost back to back home Premier League games since November 2011 when they were managed by Andre Villas-Boas.
The Toffees have only lost one of their last 11 Premier League games against the reigning champions (W6 D4); a 1-0 defeat to Manchester City in December 2014.
Wayne Rooney scored his 200th Premier League goal in Everton’s 1-1 draw at Manchester City on Monday night. He managed this feat in his 462nd game, while the only other player to reach 200; Alan Shearer (260), did this in 306 matches.
Everton had eight English players in their starting XI for their last Premier League game at Manchester City. One of the eight players in their last match was Tom Davies, who wasn’t born when Everton last did this on Boxing Day 1997.
TV COVERAGE & KICK-OFF TIME
The match kicks off at 13:30 BST but it is not due to be shown live in the UK. The game's highlights will be first televised on BBC's Match of the Day 2, which airs at 22:35.