What is the Hebrew word for chosen one?

There isn't a single word with this meaning, and the translation of "chosen" depends on context. For example:

chosen door = delet nivcheret (דלת נבחרת)

chosen food = ochel nivchar (אוכל נבחר)

chosen people = am segulah (עם סגולה)

If you mean "Chosen One" as in the person who has been selected by fate to fulfill an important task (such as Anakin Skywalker, Harry Potter, or Neo in their respective universes), the term is: ha-nivchar (הנבחר)