French port receiving a quantity of chicken (6)
I believe the answer is:
breast
'quantity of chicken' is the definition.
(a single chicken breast)
'french port receiving a' is the wordplay.
'french port' becomes 'brest' (port city in Brittany).
'receiving' is an insertion indicator.
'brest' enclosing 'a' is 'BREAST'.
(Other definitions for breast that I've seen before include "face" , "Joint of chicken" , "Reach the top of (a hill)" , "Part of a jacket" , "Bit of turkey, perhaps" .)