Many a complaint has a culinary connection (6)
I believe the answer is:
Here is my best explanation:
'a culinary connection' is the definition.
Although both the answer and definition are singular nouns, I cannot see how they can define each other.
'many a complaint' is the wordplay.
'many a' becomes 'c' (I am not sure about this - if you are sure you should believe this answer much more).
'complaint' becomes 'hives' (I've seen this before).
'has' is the link.
(Other definitions for chives that I've seen before include "Herb of the onion family", "Plants", "Plant of onion family", "Herbs with long tubular onionflavoured leaves" and "Leaves used as onion-flavoured seasoning".)