No. Since the Champions League has become a League format, Everton has never even got past the qualifying stage.
And if you count the European Cup before it became the Champions League, Everton has still not won it.
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Not the premier league no. The only teams to have won that are Man United, Chelsea, Arsenal and Blackburn. Everton have however won the top division 9 times in their history, the most recent title being in 1987