One's oddest feature (4)
I believe the answer is:
nose
'feature' is the definition.
(I've seen this before)
'one's oddest' is the wordplay.
'oddest' is an anagram indicator (I've seen 'odd' mean this).
'ones' is an anagram of 'NOSE'.
(Other definitions for nose that I've seen before include "front part of vehicle" , "Organ of face" , "Front of an aircraft" , "Don't cut this off to spite your face" , "Olafactory organ" .)