State oil’s coming from mouth? (6)

I believe the answer is:

greece

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'state' is the definition.
(I know that Greece is a type of Balkan country)

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for greece that I've seen before include "European state" , "Zorba's land" , "Southern European country" , "Country of Hellenes" , "Bust area" .)

I've seen this clue in The Times.

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