Chapter in story backed great success (5)
I believe the answer is:
eclat
'great success' is the definition.
(I've seen this before)
'chapter in story backed' is the wordplay.
'chapter' becomes 'c'.
'in' means one lot of letters goes inside another.
'story' becomes 'tale' (synonyms).
'backed' says the letters should be written in reverse.
'c' going within 'tale' is 'talce'.
'talce' back-to-front is 'ECLAT'.
(Other definitions for eclat that I've seen before include "Showy effect (Fr.)" , "Universal approval" , "Brilliance" , "great success" , "Splendour; renown" .)