The 22-year-old scored the opening goal for the Blues in their Premier League clash against Bournemouth at Stamford Bridge.
Nicolas Jackson did excellently to run through the Cherries' midfield and find Palmer, whose finish was cool and calm.
He has now been involved in 20 Premier League goals this season with 14 goals and six assists coming his way in Chelsea colours.
This is second only to Liverpool forward Mohamed Salah, who leads on 31 with 18 goals and 13 assists.
Palmer still has some way to go in order to match his efforts from last season when he hit 33 goal contributions in the league.
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However, he is the first Chelsea player to hit 20 or more Premier League goals and assists in consecutive campaigns since Hazard.
The Blues legend did so in his first three seasons with the club after signing from Lille, which were in 2012/13, 2013/14 and 2014/15.
Hazard amassed 139 Premier League goal contributions in total for Chelsea during his seven-year stint in west London.
Palmer is on 53 after just a season-and-a-half with the Blues, a tally that looks set to increase further in the coming years.
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He had a brief injury worry shortly after his goal though as he went down holding his ankle after a challenge on Antoine Semenyo.
However, Palmer was able to return to the action following a short wait on the touchline.
Bournemouth came so close to equalising but Justin Kluivert's low effort came off the post.
Jackson went on a blistering run seconds later and then hit the woodwork himself during a dramatic run of play.