From Marvel Studios News:
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Directors Joe and Anthony Russo have officially marked January 23, 2017 as the first day of production on Avengers: Infinity War. They made the announcement on their official Facebook page along with a photo that proves we’ll be happy with any Infinity War trailers they’re willing to share.
The Russos Brothers specifically mentioned “Infinity” in their post, but in theory, this also marks the beginning of production on the untitled fourth Avengers movie previously known as Avengers: Infinity War Part II. Despite the title change, the fourth Avengers movie is still being filmed along with Infinity War as part of one massive production that will cover most of 2017.