Blues boss Maurizio Sarri no longer appears at immediate risk of being sacked, but the same is not true of opposite number Marco Silva, who could do with a positive result to take into the international break.
Much was expected of Everton this season after finally landing their top managerial target in Silva, though with just two months to go the Toffees' campaign is badly petering out.
Seventh was always ultimately the most Silva could aim for in his first season at Goodison Park, but even that target now looks out of reach as his side trail Wolverhampton Wanderers by seven points.
Last week's 3-2 loss at Newcastle United, in a match that Everton led by two goals with just over 25 minutes to play, leaves them in the bottom half of the table and serious questions are now being asked of the manager.
The pressure is clearly starting to get to Silva, who cost Everton a £4m compensation fee after they made an illegal approach to Watford, as he confronted referee Lee Mason at the end of the match at St James' Park and now faces a touchline ban.
With a two-week break to come after this weekend's match, there are suggestions that Everton could be about to cut their losses just 10 months into the Portuguese's tenure. Victory, then, or a hard-earned draw, has to be the target.
Everton may have claimed a point against city rivals Liverpool in their most recent home outing, and they also had little trouble in seeing off Cardiff City 3-0 in South Wales three weeks ago, but they have taken just 15 points from the last 51 on offer.
Throw an embarrassing FA Cup exit at the hands of second-tier Millwall into the mix, and it is clear to see why this is turning into such a frustrating campaign for supporters.
Furthermore, the Merseyside outfit have won just one of their last eight Premier League home games, losing half of those, and they have not defeated a big-six side in the league since January 2017, drawing seven and losing 18 in that sequence.
With Chelsea, Arsenal, Manchester United and Tottenham Hotspur still to play in their remaining eight matches, three of those at home in successive matches, Everton need to find some form from somewhere to drag themselves back up the table.
Recent form in Premier League: LLLWDL
Sarri will be grateful that his side are no longer the media's 'crisis club' of choice, having seen his side go five matches without defeat - seven if you include the EFL Cup final against Manchester City, which finished 0-0 after 180 minutes.
Chelsea lost that tie on penalties to deny Sarri his first silverware in English football, but the manner of his side's performance - two weeks on from losing 6-0 to the same side in the Premier League - ensured that he was given a couple more games to prove himself.
The Blues have since cruised past Dynamo Kiev to qualify for the last eight of the Europa League, as well as taking seven points from league games against Tottenham Hotspur, Fulham and Wolverhampton Wanderers.
Sarri would have been disappointed to only come away with a 1-1 draw against Wolves, but even that had a feel-good nature to it as Eden Hazard struck a couple of minutes from the end to cancel out Raul Jimenez's breakaway opener.
Wolves had just one real effort of note all afternoon last weekend, though that will surely not be the case with Everton at Goodison Park as the Toffees will be under pressure to attack in front of their supporters.
If the draw with Wanderers was a frustrating day on the whole for Chelsea, then Thursday night's trip to Dynamo Kiev for the second leg of their Europa League last-16 tie offered a perfect chance to let off some steam.
Olivier Giroud scored a perfect hat-trick, Marcos Alonso netted one and Callum Hudson-Odoi again showed why he is so highly rated as the West Londoners ran out 5-0 winners on the night, 8-0 winners on aggregate.
Winning the Europa League and finishing fourth in the Premier League would make this a positive first season for Sarri, who it must be remembered has improved Chelsea's points tally from this stage 12 months ago.
Chelsea's top-four fate is still in their hands, even if they do currently reside in sixth, as they have a game in hand against Brighton & Hove Albion to fit in between now and the end of the season.
With Arsenal, Manchester United and Tottenham not in action this weekend, this is Chelsea's big chance to potentially climb a couple of places and move to within a point of third, leaving the Blues nicely positioned heading into the final stretch of an up-and-down season.
Recent form in Premier League: LWLWWD
Recent form (all competitions): LWWWDW
Gonzalo Higuain was forced to sit out the midweek meeting with Dynamo Kiev due to illness, and he now faces a battle to win back his place through the middle following Giroud's hat-trick at the NSC Olimpiyskiy.
At no ground has Hazard played more Premier League games without scoring than he has at Goodison Park, though - six, level with Selhurst Park.
Seamus Coleman was named in Everton's starting lineup to face Newcastle but pulled out of the squad because of illness. That is unlikely to keep him out this weekend, however, meaning Jonjoe Kenny should drop down to the bench.
Theo Walcott, another player in contention to start, has scored six goals in all competitions against Chelsea, netting at least once in all four grounds he has faced them at.
Everton possible starting lineup:
Pickford; Coleman, Keane, Mina, Digne; Gueye, Gomes; Richarlison, Sigurdsson, Bernard; Calvert-Lewin
Chelsea possible starting lineup:
Kepa; Azpilicueta, Rudiger, Luiz, Emerson; Kante, Jorginho, Barkley; Pedro, Giroud, Hazard
Head To Head
Everton are winless in their last six Premier League meetings with Chelsea, failing to score in each of the last five. Not since between 1972 and 1979 have they gone on a longer run without scoring against a single opponent (seven vs. Southampton).
The Blues are unbeaten in their last two away league visits to Goodison Park, though they have not managed three in a row since a run of eight between 2001 and 2008.
The last two Premier League meetings between Everton and Chelsea have finished 0-0. Only four fixtures in the competition's history have finished goalless in three consecutive games (Arsenal vs. Queens Park Rangers, Aston Villa vs. Manchester United, Charlton Athletic vs. Middlesbrough and Coventry City vs. Sheffield Wednesday).
We say: Everton 0-1 Chelsea
Chelsea have lost three of their last seven Premier League games, as many as they had in their first 22 this season, but they do appear to have turned a corner over the past few weeks. Everton boss Silva has a poor managerial record against the top six, taking just three points in his last 12 Premier League games against the division's elite, and we are expecting his side to come out second best on Sunday.