To do that, they must destabilise Jose Mourinho's title charge. In the Premier League, only two sides have avoided defeat at Chelsea all season, while the Londoners are unbeaten in 11 league games, winning eight.
Here's a look ahead to Saturday's key bout from an Everton perspective.
Two Schools of Thought
For this match, Roberto Martinez will be tempted to change his preferred possession-based approach in favour of a more direct, counter-attacking brand of football.
At home, Chelsea are likely to dominate time on the ball. They average 58 percent possession at home and registered 56.5 percent in September's fixture at Goodison Park—the most any side has managed against Martinez's Everton.
Clearly, keeping hold of the ball will be tough, although that won't be any measure of success on Saturday.
In recent away games, the Toffees have gained control through possession without finding enough cutting edge in attack—as was the case at Spurs, Liverpool and Stoke.
Liverpool Result a Reason to Change
Additionally, Everton's humiliating 4-0 loss at Liverpool strengthens the argument to adapt for this specific game.
The Toffees were far too attacking against their rivals and were regularly caught on the break—something Chelsea's roster could easily repeat.
As this clip highlights, too often Martinez saw his side caught in possession and then outnumbered at the back.
Liverpool had penetrative, pacey options in attack that thrived against Everton's system, as the following clip also demonstrates.
The fact Chelsea have such similar threats, and recorded their own master-class of counter-attacking football against Manchester City, should serve as a warning to Martinez.
Playing the same way against Mourinho's explosive forwards is asking for trouble.
Defend Narrow, Force Chelsea Wide
In this less accommodating approach, a lot of Everton's work will come without the ball.
During most phases of play, 10 of 11 players would be behind the ball, as is shown from this clip at Manchester United.
Everton's 4-2-3-1 shape is clear to see. Gareth Barry and James McCarthy condense the space in the middle, the back four remain narrow and the three attacking midfielders tuck in but remain poised to break.
The opposition are forced wide and left resorting to crosses and long-range efforts. This was how the Toffees set up having taken the lead in September's clash with Chelsea, which proved effective.
Chase the Turnover, Attack the Space
Barry and McCarthy will be especially important in this game. The more they can hassle the likes of Eden Hazard, Willian and Oscar, the better—especially if they can create turnovers.
With Chelsea committed in attack, Everton can create several opportunities to overload on the break, as this clip against Manchester United depicts.
Having won possession, United are caught with just three at the back as the Toffees press forward, in a similar example to Liverpool's success.
What's your prediction?
In Ross Barkley, Kevin Mirallas and Gerard Deulofeu, Everton are well armed with their own direct, incisive attackers, capable of troubling any defence.
By adopting a more cautious approach at the back, the Toffees can still prove a more dangerous proposition in attack, mimicking the way Liverpool and Chelsea have won away from home.
Dominating possession certainly doesn't guarantee any level of production.
If Everton can produce a top defensive performance, draw Chelsea onto them and combine that with a well-organised, clinical attack, they will have a better chance of success at Stamford Bridge.
Statistics via WhoScored.com