I stopped in my dealer who sold me the bike and talked to them about it and he looked over another FZ6R they had on the show room floor and he said "Yep, there is huge gap there with a lot of open chain, that's the problem..."
So, it's definitely the gap, he suggested creating some sort of...
I'm having this same issue with my pants rubbing against the chain and getting lube on them... I ruined 2 pairs of pants so far. Anyone have any other ideas that solve this issue? I normally wear semi-loose khaki pants so it's really noticeable when you get black lube on them.