US composer's chosen eccentric Austrian one (10)

I believe the answer is:

schoenberg

I'm a little stuck... Click here to teach me more about this clue!

'us composer's' is the definition.
'schoenberg' can be an answer for 'composer's' (I've seen this before). I am unsure of the 'us' bit.

'chosen eccentric austrian one' is the wordplay.
'eccentric' is an anagram indicator.
'austrian one' becomes 'berg' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'chosen' with letters rearranged gives 'schoen'.
'schoen'+'berg'='SCHOENBERG'

Can you help me to learn more?

(Other definitions for schoenberg that I've seen before include "Austrian scorer" , "Arnold --, Austrian-born composer" .)

I've seen this clue in The Independent.

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