Jose Mourinho has overseen two wins and a draw from his first three Premier League matches, while Roberto Martinez's Toffees are still looking for their first victory.
Crystal Palace was the first to do so in the maiden Premier League season, while Stoke matched the record last season on the way to drawing 15 games in the campaign - a total matched only by Everton.
Roberto Martinez's side has been held to a point by Norwich, West Brom and Cardiff so far this season, and Everton has also drawn against Chelsea in all competitions more times (52) than it has beaten its upcoming opponent (51).
Their failure to win so far this season has stemmed from an inability to convert possession and chances into goals. No side in the league has averaged a higher possession figure than Everton, with the Goodison Park outfit boasting an impressive 64.1 percent mark. The return of just two goals from 54 shots, though, signifies the troubles in front of goal.
The Toffees will hope that summer signing Arouna Kone can open his account after four scoreless games, including one League Cup tie, but midfielder Steven Pienaar might be the best bet for a goal.
The South African midfielder has scored against Chelsea in the last two encounters at Goodison Park, though the London club left Merseyside with the points last season after Frank Lampard's double saw the Blues come from behind.
Gareth Barry, signed on loan from Manchester City to fill the gap left by Marouane Fellaini's departure for Manchester United, will be pushing for his debut, as will fellow midfielder James McCarthy following his permanent move from Wigan Athletic.
Darron Gibson (knee) and Antolin Alcaraz (hernia) have returned to training but are unlikely to feature for the hosts. Striker Romelu Lukaku is not eligible to face his parent club, so will have to wait for his Everton debut.
Chelsea has shown promising signs in the early stages of the campaign, with returning manager Jose Mourinho guiding the club to two victories and a draw from the opening three fixtures. With just one goal conceded in that time, the Blues are showing many of the hallmarks that they demonstrated in the Portuguese boss' first campaign at the helm.
In 2004-05, Mourinho's Chelsea conceded just 15 goals - the fewest in Premier League history - on the way to securing the team's first top-flight title in 50 years.
Mourinho did not experience defeat against Everton in his first spell in charge at Stamford Bridge, recording four victories and two draws from their six league meetings.
Samuel Eto'o and Willian will boost Chelsea's attacking options, having both joined from Anzhi Makhachkala in the transfer window, although Fernando Torres will hope to continue up front, having scored in the UEFA Super Cup defeat against Bayern Munich at the end of August.
Eden Hazard (Achilles) has also been passed fit to play despite being withdrawn from Belgium's World Cup qualifying victory over Scotland last Friday.