Palmer put the Blues ahead at Kenilworth Road in a Premier League clash against Luton Town to continue his fine campaign.
The 21-year-old latched on to a poor pass out from the back by his former Manchester City teammate Issa Kabore before hammering in a fine left-footed strike.
He then provided an assist for Noni Madueke as Chelsea went 2-0 up at Luton before tucking in a beautiful effort after rounding the goalkeeper.
It has put him on eight goals for the season in the Premier League, as well as four assists to his name.
Palmer has both scored and assisted in four different games this season, more than any other player at Chelsea.
READ MORE ON CHELSEA
Former Chelsea star jokes club should pay fans to go as ticket prices set to increase
Pochettino likens Cole Palmer to Manchester United flop after fine Chelsea start
And only four players had previously reached double figures for goal involvements aged 21 or under in a single campaign for the Blues.
The other players to do so are Robben, who scored seven times and assisted nine in his debut season at Stamford Bridge in 2004/05.
Hazard also achieved the feat in his debut year, scoring nine and assisting 14 after making the switch from Lille in 2012.
Mason Mount and Christian Pulisic were the other two players to manage 10-plus goal involvements before turning 22, Mount doing so in 2020/21 and Pulisic in 2019/20.
Most read in Football
Exclusive commentary of Luton vs Chelsea as Premier League rivals clash at Kenilworth Road
Tottenham ramp up January transfer plans with defender and midfielder targeted
League One match scrapped with fans left waiting in stands for 30 minutes in pitch black
Arsenal star Eddie Nketiah not for sale as club reject enquiry from Premier League rivals
Palmer was a shock signing at Chelsea from City, joining for £40million towards the end of the transfer window.
But he has proved any doubters wrong with excellent displays and has landed a fan in the talkSPORT building.
Speaking on talkSPORT live on air, former West Ham United and Norwich City striker Dean Ashton said: "What a gift he's been from Manchester City.
"It was a big surprise when he turned up at Stamford Bridge and has by far been their best attacking player.
"We saw two examples there. Jackson went through and it was just a tame, sidefooted effort.
"If he was going to go for that then it needed to be whipped into that far corner.
"It goes to Palmer, who sizes it up, and shows you need accuracy as he arrowed it into that far corner.
"He didn't lash at it, he just struck straight through it."
Listen to live commentary of Luton vs Chelsea on talkSPORT.