Nearby chemists supply home flu protection, might you say? (7,7)

I believe the answer is:

chimney breasts

'home flu protection might you say?' is the definition.
I know nothing about this answer so I cannot judge whether this works.

'nearby chemists supply' is the wordplay.
'supply' indicates an anagram (in a supple way).
'nearby'+'chemists'='nearbychemists'
'nearbychemists' with letters rearranged gives 'CHIMNEY-BREASTS'.

I've seen this clue in The Guardian.

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