The centre forward passed the tally of club legend Dider Drogba during the latter's first season for the club.
Drogba arrived at Chelsea when he was close to the peak of his powers, but only managed 16 goals in his first season.
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He played 41 games in that campaign, with Jackson managing 42 so far for 17 goals.
Drogba took three seasons before he managed 20 goals for the club, managing 33 goals in 60 games in the 2006-2007 campaign in all competitions.
Given Jackson is only 22, Chelsea fans will hope that he can improve a great deal.