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The new film obviously takes place before the Harry Potter movies, but exactly when does Fantastic Beasts and Where to Find Them take place? In case you couldn't tell by the fanciful dress of its characters, the movie takes place in the roaring 1920s. Specifically, it takes place in New York City in the year 1926.
More specifically, looking at the Fantastic Beasts timeline vs the Harry Potter timeline, things start to seem a lot clearer. Fantastic Beasts and Where to Find Them takes place a little over 60 years before the Harry Potter saga begins, and 54 years before Harry is even born. When the film begins in 1926, Harry, Ron, and Hermione aren't even ideas, and even Professor McGonagall hasn't yet been born.