This is a fun idea, and if done right could add a lot to the game. Playing off your thoughts you could say:
Speed chain = increased chances of higher quality drops.
Fire chain = increased attack damage of party + increased fire damage
Level chain = killing mobs x levels higher than you gives bonus to sp/xp
Same mob chain = intimadation (mobs of that type might be intimidated by your group)
While I'm sure we could go all day naming chain types, I'll let others join in if they wish, it could get pretty ridiculous pretty quickly. But sometimes it's just fun.
But also on the note of death, that would be a good penalty for dying, losing your chain(s) especially if they had it where you could get chains to a high level (50) thus making it very hard to achieve that level, but dropping all the way to zero would hurt.
And as for my example of chain level 50, it would give the highest benefit, but my thought that would only be 5% or some other bonus. Basically .1% bonus for each level.
Anyway, I agree this would open up more opportunity to party outside of leves
