Hmm..path deform is actually an interesting solution, although it'll cause deformations in the chain that aren't really ideal.
I'd say the best for what you're trying to do would be to create a bone chain (1 bone per chain link) and then use spline IK on the bones with the path, and then link each link to its respective bone. You'll be able to drag the spline IK control points around so they follow move around the path, and the chain will follow--while maintaining volume