Chilean surprisingly screens commercial for Mexican dish (9)
I believe the answer is:
enchilada
'mexican dish' is the definition.
(enchilada is a type of Mexican dish)
'chilean surprisingly screens commercial' is the wordplay.
'surprisingly' indicates an anagram (a surprising ordering of the letters).
'screens' is an insertion indicator (screen can mean to cover up).
'commercial' becomes 'ad' (abbreviation for advertisement).
'chilean' is an anagram of 'enchila'.
'enchila' going around 'ad' is 'ENCHILADA'.
'for' is the link.
(Other definitions for enchilada that I've seen before include "wrap" , "Mexican tortilla with chilli" , "Tortilla and sauce, meat" , "spicy food" , "The whole ___ -- everything (US)" .)