In this sentence, is being a participle combining with the verb chosen to
construct a gerund phrase, a verb participle that may function as a subject
Yes, exactly. Notice that "however" is set off (that is, surrounded) by commas, which means it's parenthetical (senses 2 and 3) and can safely be ignored when determining the basic structure of the sentence. With that in mind, and given that "chosen" is part of the subject, you are again correct in the comment below: In the sentence in question,
Being chosen, however, is probably not enough.
"Is" is the verb.
English sentences present some tricky problems, but analyzing them gets easier with practice. You've done a good job with this one.
The part after the verb
Now I'd like to answer your further question in the same comment below asking what the object of the sentence is.
This is another slightly tricky concept. The verb "to be" ("is" in this case) is what's called a "linking verb." What this means is that the subject is linked by the verb to something else that comes after the verb. The something else that it's linked to is called the subject complement.
If you are something, the thing that you are isn't really receiving any action by you. You've merely been renamed or described. This is in contrast to an action verb like "to hit." In the sentence "You hit a ball.", the ball is receiving your action, which is why the ball is called a direct object. A subject complement can be either a noun or pronoun, as in
"This car is a sedan."
or an adjective, as in
"This car is fast."
and it comes in exactly the same place in the sentence that a direct object would occupy. If you look up "enough" in the dictionary, you'll discover that it acts as a pronoun in this case (thank you, Man_From_India). So "enough" is the subject complement.
The comment below stating that the sentence doesn't need an object is correct. It doesn't need a subject complement either, but it does have one. Therefore the sentence without modifiers is
Being chosen is enough.
The main point to realize is that what follows the verb can't be an object, because the verb "is" is a linking verb.
You might be thinking, "Who cares what you call
the thing after the verb, whether it's an 'object' or a 'subject complement'?" This can be especially important when the subject complement is a pronoun, because personal pronouns have two cases, subjective and objective. For example,
"The professor taught her."
is a correct sentence, but
"The professor is her."
is not correct. Instead, it's correct to say
"The professor is she."
because "she" is the subjective case, just as you'd say
"She is the professor."
It should be pointed out, as Araucaria does below, that many native speakers would be more comfortable with the sentence, "The professor is her." However, upon answering the telephone, when asked "May I speak to <name>?", the response "This is she" is widely used.
(But what about the "probably not," you ask? This phrase could be analyzed a few different ways, and I don't feel qualified to write authoritatively about it. Some helpful partial answers can be found here, where I continued this line of inquiry.)