The most common and most likely answer to this crossword clue is the 8 letter word GENTILES
I've seen this crossword clue in The Guardian
G
E
N
T
I
L
E
S
Buddy explains!

The straight part
We know that "Not the chosen people" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case not the chosen people = gentiles.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does GENTILES mean?
GENTILES noun- A non-Jewish person.
- (grammar) A noun derived from a proper noun which denotes something belonging to or coming from a particular city, nation, or country.