Said to be the chief American state (5)
I believe the answer is:
maine
'american state' is the definition.
(I know that Maine is U.S. state)
'said to be the chief' is the wordplay.
'said to be' shows a homophone (sound like).
'the chief' becomes 'main' (I've seen this before).
'main' sounds like 'MAINE'.
(Other definitions for maine that I've seen before include "state of USA" , "New England state" , "Part of America" , "NE US state" , "US state, capital Augusta (5)" .)