Food, reportedly chief Chinese dish (4,4)
I believe the answer is:
chow mein
'chinese dish' is the definition.
(I've seen this before)
'food reportedly chief' is the wordplay.
'food' becomes 'chow' (chow is a kind of food**).
'reportedly' shows a homophone (sound like).
'chief' becomes 'main' (I've seen this before).
'main' is a homophone of 'mein'.
'chow'+'mein'='CHOW-MEIN'
(Other definitions for chow mein that I've seen before include "Chinese noodle dish" , "'Chinese dish with fried noodles (4,4)'" , "Chinese dish of noodles, meat and veg" , "take-away food" , "Chinese-American dish" .)