But maybe they didn't realise he'd be this good.
Palmer created history on Saturday when he became the first player to score four goals in the first half of a top-flight English match in the Premier League era.
His flurry of strikes came in Chelsea's 4-2 win over Brighton that further strengthened the belief that the London team will be a force this season after spending more than $US1 billion ($A1.4 billion) on players over the past two years.
Palmer was one of the club's expensive signings — he cost at least Stg 40 million ($50.7 million), but that looks a bargain now.
His 22 league goals last season was second only to Man City's Erling Haaland and also included a four-goal haul against Everton, and he is already up to six goals in this campaign in just six games.
How City could have done with having Palmer a few hours earlier on Saturday, when the champions drew at Newcastle 1-1 to drop points for the second straight weekend.
Man City's Erling Haaland was kept goalless for the first time this season by Newcastle defenders. (AP PHOTO)
Haaland was kept scoreless in a league game for the first time this season and stayed on 10 goals, while defender Josko Gvardiol proved their goalscorer.
Arsenal took advantage of their rivals' slip-up by beating Leicester 4-2 thanks to two stoppage-time goals — an own-goal and a close-range finish by Kai Havertz — to join City on 14 points.
But both find themselves a point behind new leaders Liverpool, who beat Wolves 2-1 thanks to a 61st-minute winner by Mohamed Salah from the penalty spot.
Brentford became the first Premier League team to score inside the first minute in three straight games, but still couldn't hold on following Bryan Mbeumo's strike after 37 seconds as they went on to draw with West Ham 1-1.
Everton finally gained their first win of the season, beating Crystal Palace 2-1 thanks to two goals by Dwight McNeil, while Fulham won at Nottingham Forest 1-0, with Mexico striker Raul Jimenez scoring in a third straight game.
At Newcastle, it was City's first league match since influential midfielder Rodri was ruled out for the season with an ACL injury sustained in the 2-2 draw against Arsenal last weekend and the champions were far from their fluid best without the Ballon d'Or contender.
Haaland barely got a chance at St. James' Park, so couldn't tie the record of City great Sergio Aguero in scoring in each of his first six games of a Premier League season.
Gvardiol put City ahead in the 35th minute before Anthony Gordon converted a penalty for Newcastle's equaliser in the 58th.
Arsenal had been dejected by a stoppage-time equaliser for City last weekend, but six days later were celebrating late goals of their own after winless Leicester threatened to pull off an unlikely comeback draw at Emirates Stadium.
Gabriel Martinelli and Trossard scored for Arsenal in the first half, only for the Gunners to let in two goals from Leicester right back James Justin.
But Arsenal went back in front in the fourth minute of stoppage time through Leandro Trossard before Havertz bundled in the fourth in the 99th minute.
Mohamed Salah slots home Liverpool's winner from the penalty spot. (AP PHOTO)
A league-high fifth win for Liverpool didn't come easy against Wolves at Molineux.
They needed Salah to convert their winner from the spot after a foul by Nelson Semedo on former Wolves player Diogo Jota, who was booed throughout.
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