Oddly, Maine's not an American state! (9)
I believe the answer is:
minnesota
'an american state' is the definition.
(Minnesota is an example)
'oddly maine's not' is the wordplay.
'oddly' is an anagram indicator.
'maines'+'not'='mainesnot'
'mainesnot' with letters rearranged gives 'MINNESOTA'.
(Other definitions for minnesota that I've seen before include "Superior neighbour" , "Wobegon state (Keillor)" , "source of iron ore" , "North Star State" , "US state, capital St Paul" .)