I agree with you that the Champions League is comprises of all big and best teams across Europe, but I don’t agree with you that Chelsea is not one of them because Chelsea is a big team because it has won the Champions League before now and can win it again.
With this current Chelsea squad, I am sure they will go very far in the champions league next season.
Chelsea are two times champions league winners therefore nobody should be saying Chelsea isn't a big team. Not many teams have won more trophies than Chelsea. Just because they were going through some difficult times doesn't mean they're not a big club. An example is Manchester United, they have been awfully recently but still a big team. History can't just be forgotten because it's history that makes clubs big. There are some clubs that are just becoming big recently but the ones that have being doing it for a long time can't be disregarded. Chelsea have a good squad now and I won't be surprised if Chelsea end up winning the champions league.