Greece won the UEFA EURO 2004 in Portugal after a win against
Portugal in the final resulting in a 1-0 score.
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The uefa cup is a club competition. Greece is a national team. A
Greek club has never won this title as far as I know. Greece did
win the uefa Euro 2004 competition. They beat the host team
Portugal 1-0.
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Yes, Greece won the UEFA European Football Championship (Euro Cup) in 2004.