The youngster continued to prove himself as one of the best players in the world with four goals inside 20 minutes during the first half - becoming to first Premier League player to achieve such a feat.
Palmer first showed good composure to convert after having the ball squared to him by Nicolas Jackson, before converting a penalty and then a stunning freekick all inside 10 minutes.
He added a fourth just 10 minutes later, drilling a superb strike in at the near post to completely stun Brighton - and the majority of the country.
Palmer has been in excellent form this season and already has five goals and four assists in six Premier League games.
Chelsea will look to continue their strong start to the campaign when they face Nottingham Forest on Sunday, 6th October.