Josh O'Connor filmed the first half of La Chimera prior to filming his role as Patrick Zweig in Challengers, then returned to Italy to complete the second half.
Alice Rohrwacher initially envisioned Arthur as an older man, so she wasn't thinking of Josh O'Connor as the right casting. However, after meeting, she thought Connor was an old soul, so she ended up casting him as Arthur.
Josh O'Connor wanted to work with Alice Rohrwacher, so he ended up writing to her five times over the course of three years. He didn't know her address, so he just put 'Italy', which made only one letter arrive.