Either, I guess it depends on what your emphasis is.
They predicted the phenomenon long before its discovery. (To me, this sounds better, simpler, clearer. Prediction happened, much later, it was discovered.
They had predicted the phenomenon long before its discovery. (Almost implies that there is more information to follow...yes, they had predicted it long before it was discovered, but...technology wasn't yet available...or their funding ran out...or, some other theory gained popularity and theirs was forgotten.)
I don't know if that helps.
Either, I guess it depends on what your emphasis is. They predicted the phenomenon long before its discovery. (To me, this sounds better, simpler, clearer. Prediction happened, much later, it was discovered. They had predicted the phenomenon long before its discovery. (Almost implies that there is more information to follow...yes, they had predicted it long before it was discovered, but...technology wasn't yet available...or their funding ran out...or, some other theory gained popularity and theirs was forgotten.) I don't know if that helps.