" It is also correct if you eliminate "being" as you have asked. Whether "chosen" is an adjective or not is interesting. We have a passive construction here.
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Amir OghlowIs chosen in this sentence an adjective?No. It is a verb. The distinction between verb forms and adjectives is rather complicated, and different linguists have different takes on it. It may benefit you to read CJ's answer in this thread, since you seem to be focused on adjectives versus passive forms.