The Portuguese has overseen two wins and a draw from his first three Premier League matches, while the toothless Toffees are still looking for their first victory
Crystal Palace were the first to do so in the maiden Premier League season, while Stoke matched the record last term on their way to drawing 15 games in the campaign - a total matched only by Everton.
Roberto Martinez's side have been held by Norwich, West Brom and Cardiff so far this season, and they have also drawn against Chelsea in all competitions more times (52) than they have beaten them (51).
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No side in the division has averaged a higher possession figure than Everton, with the Goodison Park outfit boasting an impressive 64.1 per cent, while their return of two goals from 54 shots underlines their troubles in front of goal.
They will hope that close-season signing Arouna Kone can open his account after four scoreless games, including one League Cup tie, but midfielder Steven Pienaar might be their best bet for a goal.
The South African midfielder has scored against Chelsea in their last two visits, though the London club left Merseyside with the points last season after Frank Lampard's double saw them 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 have shown promising signs in the early stages of the campaign, with returning manager Jose Mourinho guiding them to two victories and a draw from their opening three fixtures.
With just one goal conceded in that time, they 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 their way to securing their 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.