Execute mythical king in US chain (7)

I believe the answer is:

dominos

'us chain' is the definition.
(US pizza takeaway chain)

'execute mythical king' is the wordplay.
'execute' becomes 'do' (doing is a kind of executing).
'mythical king' becomes 'Minos' (mythical king of Crete).
'do'+'minos'='DOMINOS'

'in' is the link.

(Another definition for dominos that I've seen is " Cloaks".)

I've seen this clue in The Guardian.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.