No one has scored a treble in three consecutive English top-flight games since Liverpool's Jack Balmer in 1946.
The only other players to achieve the feat were Tottenham Hotspur's Frank Osborne in 1925 and Tom Jennings of Leeds United in 1926.
Ivory Coast international Drogba helped to wrap up the Premier League title for Chelsea on the final day of last season when he bagged three goals in an 8-0 demolition of Wigan at Stamford Bridge.
Drogba then started the new campaign with another treble in a 6-0 rout of promoted West Bromwich Albion last Saturday.
The 32-year-old's second hat-trick in a row helped him surpass Jimmy Greaves's total of 132 goals as Chelsea's sixth-highest scorer.
"I didn't know (about the record) but it is really nice," Drogba told the club's website.
"I have said I want to make history in the club and by being among these big players I have done it. But I don't want to stop here, I want my name as high as I can (get it)."
Only Bobby Tambling (202), Kerry Dixon (193), Frank Lampard (158), Roy Bentley (150) and Peter Osgood (150) are ahead of Drogba (134) on Chelsea's all-time list.
Wigan will be wary of the Ivorian especially as Roberto Martinez's team had the second-worst defensive record in the Premier League last season and slumped to a shock 4-0 home defeat by promoted Blackpool last Saturday.
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