The Blues missed the opportunity to claim a second straight victory in last Sunday's meeting with Sheffield United at Bramall Lane.
Jayden Bogle levelled after Thiago Silva had given Chelsea the lead, before Noni Madueke saw his effort cancelled out by Oli McBurnie's 93rd-minute equaliser.
Chelsea are finding it tough to strike a balance between attack and defence, having found the net at will in recent weeks while leaking goals at an alarming rate.
As a result, the Blues could become the first team in English football history to score and concede at least twice in eight consecutive matches.
Chelsea's current run began with a 3-2 FA Cup win over Leeds United, before they played out a 2-2 draw with fellow West London club Brentford.
Mauricio Pochettino's side then beat Newcastle United 4-3 and Leicester City 4-2 in the Premier League and FA Cup respectively.
After rounding off March with a 2-2 draw against Burnley, Chelsea claimed a dramatic 4-3 win over Manchester United before they faced Sheffield United last weekend.
Although they have failed to keep a clean sheet in 13 consecutive matches, the Blues will be pleased with the fact that they have gone seven games without defeat since losing to Liverpool in the League Cup final.
Fortress Stamford Bridge
Chelsea will be confident about their chances of extending their unbeaten run, having fared well in recent home meetings with the Toffees.
The Blues have avoided defeat in each of their previous 28 Premier League home matches against Everton, representing their longest unbeaten home streak against a single opponent in their top-flight history.
However, Chelsea have had to settle for draws in each of their last two head-to-head home games, including a 2-2 scoreline in last season's clash at Stamford Bridge.
After losing 2-0 in the reverse fixture, Chelsea are at risk of losing two league games to Everton in a single season for the first time in 45 years.
With the Blues looking to avenge December's defeat at Goodison Park, they will hope Cole Palmer can produce another strong performance as he bids to become the first Chelsea player to score in seven successive Premier League home matches.