The UEFA Champions League was expanded in 1997-98 to allow eight non-champions to enter (each were runners-up of their domestic league in the previous season). Which team was the first to play in a Champions League Final, having never won a domestic title?

Bayer Leverkusen in 2002:
they had finished as runner-up in the Bundesliga four times until then, without winning the title (they still haven't) : https://en.wikipedia.org/wiki/Bundesliga
They lost to Real Madrid in the 2002 final.

Bayer Leverkusen (in 2002) is the only club to play in the final having never won their domestic league.

https://en.wikipedia.org/wiki/European_Cup_and_UEFA_Champions_League_records_and_statistics

In the 1979/1980 season of the European Cup, which was the predecessor of the Champions League, Nottingham Forest not only made it to the final but also won the whole thing without being a national champion the preceding season. Nottingham was qualified as winners of the 1978/79 European Cup, to which they in turn qualified as winners of the English top division 1977/78. (It wasn't called Premier League at that time.) I believe, but can't guarantee, that Nottingham Forest at the time was the only team to win the European Cup more times than the national championship.

(Not claiming that the first answer was wrong, just adding a bit of interesting information about the predecessor of Champions League.)