Stretching string will not give any power at all, in fact it will rob bow out of energy, as some energy is required for stretching the string, obviously.
Lack of stretchability is one of most desired qualities of good string, of course it's often hard to balance with resilience - if string won't snap, it usually must stretch a tiny little bit at least.
As far as chain goes, I can't imagine how should it work.
Aside from problems with achieving any sort of good tension with chain, after release every link would obviously move a bit in random direction, making it all pointless.
Adding the fact that metal chain would be obviously terribly heavy for string... Bad idea in general.