Palmer, 21, has been a revelation since arriving in west London from Manchester City last summer and continued his stunning form against Sean Dyche’s Toffees.
The England international nutmegged Everton defender Jarrad Branthwaite before placing a precise strike past Jordan Pickford to give Chelsea the lead on 13 minutes.
Five minutes later, Palmer headed home into an empty net after Nicolas Jackson’s shot was only half-saved by Pickford.
Palmer completed his perfect hat-trick inside 30 minutes as he intercepted a poor pass from Pickford and lifted a delightful lob over the England goalkeeper and into the net.
‘If there is anybody in the Premier league you don’t want to give the ball to in that situation it is Cole Palmer,’ ex-Arsenal striker Alan Smith said on the Sky Sports commentary.
‘Palmer cannot believe his luck here, he takes it like it was the easiest chance in the world. He is playing with such confidence, he is bossing it.’
Palmer’s performance against Everton also saw him become the first ever Chelsea player to score in seven successive Premier League matches at Stamford Bridge.
In his most recent home appearance, Palmer scored two injury-time goals in another hat-trick to stun Manchester United in a dramatic and thrilling 4-3 win.
Chelsea added a fourth before half-time through Jackson, who took down a cross before swivelling and beating Pickford with a superb finish.
More to follow…
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