Surprisingly tiny chest that's not natural (9)
I believe the answer is:
synthetic
'not natural' is the definition.
(something synthesised is not natural)
'surprisingly tiny chest' is the wordplay.
'surprisingly' indicates anagramming the letters (a surprising ordering of the letters).
'tiny'+'chest'='tinychest'
'tinychest' is an anagram of 'SYNTHETIC'.
'that's' is the link.
(Other definitions for synthetic that I've seen before include "Not natural in origin" , "Artificially made" , "Artificially produced" , "Affected" , "Artificially-made compound" .)