Brilliant success of a tale about the capital of Chile (5)
I believe the answer is:
eclat
'brilliant success' is the definition.
(I've seen this in another clue)
'a tale about the capital of chile' is the wordplay.
'about' is an anagram indicator.
'the capital of' indicates taking the first letters.
The initial letter of 'chile' is 'c'.
'tale' anagrammed with 'c' gives 'ECLAT'.
'of' is the link.
(Other definitions for eclat that I've seen before include "Cleat (anag.)" , "Splash" , "French renown" , "Splendour; renown" , "Distinguished success" .)